« r 


CHAUNCEY  WETMORE  WELLS 

1872-1933 


This  book  belonged  to  Chauncey  Wetmore  Wells.  He  taught  in 
Yale  College,  of  which  he  was  a  graduate,  from  1897  to  1901,  and 
from  1 90 1  to  1933  at  this  University. 

Chauncey  Wells  was,  essentially,  a  scholar.  The  range  of  his  read- 
ing was  wide,  the  breadth  of  his  literary  sympathy  as  uncommon 
as  the  breadth  of  his  human  sympathy.  He  was  less  concerned 
with  the  collection  of  facts  than  with  meditation  upon  their  sig- 
nificance. His  distinctive  power  lay  in  his  ability  to  give  to  his 
students  a  subtle  perception  of  the  inner  implications  of  form, 
of  manners,  of  taste,  of  the  really  disciplined  and  discriminating 
mind.  And  this  perception  appeared  not  only  in  his  thinking  and 
teaching  but  also  in  all  his  relations  with  books  and  with  men. 


FIVE-PLACE 

LOGARITHMIC  AND  TRIGO 

NOMETRIC  TABLES 


EDITED  BY 


JAMES  M.  TAYLOR,  A.M.,  LL.D. 

Colgate  University 


•  •    ••••••. 


•••  ••  •  • 


GINN  AND  COMPANY 

BOSTON    •    NEW   YORK     •    CHICAGO     •    LONDON 
ATLANTA     •    DALLAS     •    COLUMBUS     •    SAN   FRANCISCO 


COPYKIGHT,  1905 

By  JAMES  M.  TAYLOR 


ALL  BIGHTS  RESEKVED 
521.6 


«    e    ccr*        •«• 


IN  MEMORIAM 


GINN  AND  COMPANY*  PRO- 
PRIETORS  •  BOSTON  •  U.S.A. 


PEEFACE 


The  editor's  aim  in  these  tables  has  been  to  secure  an  open  and 
attractive  page,  an  arrangement  easily  understood  but  not  involving 
needless  repetitions,  and  some  simple  device  by  which  any  required 
data  in  the  table  can  be  quickly  found.  By  lessening  the  time  and 
weariness  involved  in  using  logarithmic  tables,  it  is  hoped  that  log- 
arithmic computation  will  be  encouraged  and  made  more  attractive 
to  the  beginner. 

These  tables  are  intended  primarily  for  those  who  use  logarith- 
mic and  trigonometric  tables  for  the  first  time.  The  editor  believes 
that  clearness  of  comprehension  of  the  tables  by  beginners  is  pro- 
moted by  retaining  the  decimal  point  before  mantissas  and  by  tabu- 
lating the  exact  characteristics  of  the  trigonometric  functions.  In 
§  6,  simple  rules  are  given  for  the  characteristics  of  the  logarithmic 
functions  of  angles  between  6°  and  84°.  The  computer  should 
apply  these  fundamental  rules  so  that  when  the  given  angle  is 
between  these  limits  he  will  seek  only  the  mantissas  of  its  func- 
tions in  thQ  table,  and  will  know  at  once  the  relation  of  an  angle 
to  45°  from  the  characteristic  of  its  logarithmic  tangent  or  cotan- 
gent.   Moreover,  these  rules  are  useful  as  simple  checks. 

In  Tables  III  and  IV  characteristics  are  written  only  at  the  top 
and  the  bottom  of  each  column  of  mantissas.  Even  these  are 
superfluous  when  the  angle  is  between  6°  and  84°.  In  Tables  I,  III, 
and  IV  the  first  two  figures  of  a  mantissa  are  written  only  in  the 
first  mantissa  having  these  figures  and  in  the  first  mantissa  of 
each  group  of  five  m^antissas.  This  plan  makes  the  printed  figures 
stand  out  clear  and  distinct  in  an  open  page,  greatly  aids  the  eye  in 
following  either  rows  or  columns,  and  practically  reduces  groups 
of  five  mantissas  to  groups  of  four.  In  using  such  tables  the  student 
is  not  fatigued  through  the  strain  and  confusion  incident  to  con- 
sulting pages  crowded  with  needlessly  repeated  figures. 

To  enable  the  computer  to  find  at  once  the  page  or  the  part  of  a 
page  on  which  any  given  datum  is  tabulated,  each  table  is  provided 
with  a  system  of  tabs.  The  explanation  of  these  tabs  in  §§  10-13 
will  contribute  to  the  better  understanding  of  the  tables  themselves, 
and  their  use  will  lead  the  student  to  a  method  in  his  work  and 
enable  him  to  find  any  desired  data  in  the  tables  in  less  than  half 
the  time  usually  required.  j^^^^^^  ^    ^^^^^^^^ 

Colgate  University,  December,  1905 

iii 


863f7y3 


CONTENTS 

Tables  Pages 

Explanation  of  tables v-xvi 

I.    Five-place  mantissas  of  the  logarithms  of  the  entire  numbers 

from  1  to  11,000 1-21 

II.    The  values  and  logarithms  of  important  constants      ....         22 

III.  Five-place  logarithms  of  the  sines,  cosines,  tangents,  and  cotan- 

gents of  angles  from  1°  to  89°  for  each  minute 23-45 

IV.  Five-place   logarithms  of  sines,  cosines,  tangents,  cotangents 

Of  angles  from  0'  to  3'  for  each  second 46 

Of  angles  from  3' to  2°  for  every  ten  seconds       ....  47-52 

V.    Four-place  values  of  the  sines,  cosines,   tangents,   and  cotan- 
gents of  angles  from  0°  to  90°  for  each  minute 53-71 

VI.    The  logarithms  S  and  T  for  angles  less  than  2° 72 


EXPLANATION  OF  TABLES 


Table  I 

1.  Table  I  contains  five-place  mantissas  of  the  common  loga- 
rithms of  all  entire  numbers  from  1  to  11,000.  Mantissas  can  be 
expressed  only  approximately,  and  in  a  five-place  table  all  the  fig- 
ures which  follow  the  fifth  are  rejected,  the  fifth  being  increased 
by  1  whenever  the  sixth  figure  is  5  or  more. 

When,  after  the  fifth  figure  has  been  increased,  the  last  signifi- 
cant figure  in  a  mantissa  is  5,  it  is  printed  with  a  bar  under  it. 
Hence  in  the  fifth  place  5  indicates  that  the  fifth  figure  was  4  and 
the  sixth  5  or  more ;  in  the  fourth  place  5  indicates  that  the  fourth 
figure  was  4,  the  fifth  9,  and  the  sixth  5  or  more ;  and  so  on. 

When  their  place  is  blank  the  first  two  figures  of  any  mantissa 
are  the  two  figures  first  above  the  blank  space. 

Note.  For  brevity  in  the  following  pages  we  shall  call  the  decimal  part  of 
the  logarithm  of  a  number  the  mantissa  of  the  number,  and  the  integral  part 
of  the  logarithm  the  characteristic  of  the  number. 

2.  To  find  from  the  table  the  mantissa  of  any  whole  number. 
We  have  the  two  following  cases. 

(a)  When  the  given  number  is  less  than  11,000,  that  is,  when  the 
number  is  in  the  table. 

E.g.^  let  the  number  be  7423.  On  page  14,  in  the  column  headed  "N,"  we 
find  the  first  three  figures,  742  ;  passing  along  this  line  or  row  to  the  column 
with  the  fourth  figure,  3,  at  its  top,  we  find  .87058,  which  is  the  mantissa 
of  7423. 

Thus  the  first  three  figures  of  a  number  of  four  figures  give  the 
rotv,  and  the  fourth  figure  gives  the  column  in  which  the  mantissa 
is  found. 

When  the  number  is  one  of  less  than  four  figures,  by  adding  one  or  more 
ciphers  we  obtain  a  number  of  four  figures  whose  mantissa  is  the  same  as  that 
of  the  given  number. 

E.g.^  the  mantissa  of  59  =  the  mantissa  of  5900  =  .77085. 

To  save  time  in  finding  the  mantissa  of  a  number  of  one  or  two  figures,  the 
mantissa  of  each  whole  number  from  1  to  100  is  given  on  page  1  in  the  column 
headed  "M,"  at  the  right  of  the  number  itself  in  the  column  headed  "  N." 


vi  EXP^NATIO^OF  TABLES 

Ex.  1.  Find  log  8300  and  log  O.obdsi' 

The  characteristic  of  8300  is  +3,  and  that  of  0.00083  is  -4,  or  6  -  10. 
The  mantissa  of  8300  or  0.00083  is  the  same  as  the  mantissa  of  83. 
The  mantissa  of  83  =  .91908. 
Hence        log  8300  =  3.91908, 
and  log  0.00083  =  4.91908,  or  6.91908  -  10. 

If  the  number  lies  between  10,000  and  11,000,  its  mantissa  will 
be  found  on  page  20  or  21.  Here  the  first  fotir  figures  of  the  num- 
ber give  the  row,  and  ilnQ  fifth  figure  gives  the  column  in  which  the 
mantissa  is  found. 

E.g.,  the  mantissa  of  10315  =  .01347. 

Note.     For  the  explanation  of  the  marginal  tabs  of  Table  I  see  §  10. 

Ex,  2.  Verify  each  of  the  following  identities : 

log  4354   =  3.63889  ;  log  62.81  =  1.79803  ;  log  37.96    =  1.57933  ; 
log  945.8  =  2.97580  ;  log  0.749  =  1.87448  ;  log  10.327  =  1.01397. 

(h')  When  the  given  number  is  greater  than  11,000,  that  is,  when 
the  number  is  not  in  the  table. 

In  this  case  we  assume  that  any  small  increase  in  a  number  is 
proportional  to  the  corresponding  increase  in  its  mantissa. 

This  assumption,  though  not  mathematically  exact,  is  sufficiently 
correct  for  interpolation  within  narrow  limits. 

E.g..,  let  the  number  be  54376. 

The  mantissa  of  54370  =  the  mantissa  of  5437.0. 

For  convenience  we  put,  or  conceive,  a  decimal  point  after  the  fourth  figure. 

The  mantissa  of  5438  =.73544 

The  mantissa  of  5437  =  .73536 

Hence  the  tabular  difference  =  .00008 

That  is,  for  an  increase  of  1  in  the  number  5437  there  is  an  increase  in  the 
mantissa  of  8  hundred-thousandths,  or  8  points,  as  we  may  say  for  brevity. 
Hence  for  an  increase  of  .6  in  the  number  there  will  be  an  increase  in  the  man- 
tissa of  .6  of  8  points,  or  5  points  nearly. 

Hence  the  mantissa  of  5437.6  =  .73536  +  .00005  =  .73541. 

Therefore  the  mantissa  of  54376  =  .73541. 

Ex.  3.  Find  log  27.583. 

The  characteristic  is  1,  and  the  mantissa  is  that  of  2758.3. 

The  mantissa  of  2758  =    .44059 

The  increase  for  .3  =  .3  of  16  points  = 5 

.-.log  27. 583  =  1.44064 

The  increase  for  .3  is  often  called  the  correction  for  ,3. 


EXPLANATION  OF   TABLE  I  vii 

By  aid  of  the  marginal  difference  table  this  computation  can  easily  be  made 
mentally.  E.g.^  the  mantissa  of  2758  is  .44059,  and  the  tabular  difference  is  16 
points.    In  the  marginal  table  headed  16,  in  line  3,  we  find  5,  which  is  .3  of  16. 

Ex.  4.  Verify  each  of  the  following  identities  : 

log  92.378  =  1.96557  ;  log  0.034796  =  2.54153  ; 
log  23.804  =  1.37665  ;  log  0.0030975  =  3.49101  ; 
log0.67857  =  1.83159;        log  0.075809    =2.87972. 

3.   To  find  a  number  lolien  its  logarithm  is  given. 

Keep  in  mind  that  the  mantissa  determines  the  figures  and  their 
order  in  the  expression  of  a  number,  while  the  characteristic  deter- 
mines unifs  place. 

Observe  that  the  least  and  greatest  mantissa  on  each  page  is 
written  at  the  bottom  of  the  page. 

We  have  the  two  following  cases. 

(a)  When  the  given  mantissa  is  in  the  table. 

Ex.  1.  Given  \ogx  =  2.68269,  to  find  the  value  of  x. 

On  page  9  we  find  the  mantissa  .68269  in  row  481  and  in  column  6; 
hence  .68269  is  the  mantissa  of  4816.    Since  the  characteristic  is  2,  we  have 

X  =  481.6. 

Similarly  if  \ogx  =  2.68269,  x  =  0.04816. 

Observe  that  the  first  mantissa  which  is  .68  +  or  .69  +  has  its  first  two 
figures  in  black  type  ;  this  is  to  aid  in  locating  on  the  page  any  mantissa  which 
is  between  .68  and  .69. 

Ex.  2.  Find  the  value  of  x  in  each  of  the  following  equations  : 
log  X  =  3.63889  ;  log  x  =  1. 79803 ;  log  x  =  1.57933  ; 
log  X  =  2.97580 ;  log  x  =  1.87448  ;  log  x  =  1.01397. 

For  the  answers  see  example  2  in  §  2. 

(b)  When  the  given  mantissa  is  not  in  the  table. 

Ex.  3.  Given  log  x  =  2.28250,  to  find  the  value  of  x. 

On  page  3  we  find  that  of  tabulated  mantissas  the  next  less  than  .28250  is 
.28240,  which  is  the  mantissa  of  1916. 
The  tabular  difference  is  22  points. 

The  given  mantissa  exceeds  the  next  less  mantissa  by  10  points. 
Hence  1916  should  be  increased  by  ^f  of  1,  or  0.5  approximately. 
That  is,  .28250  is  the  mantissa  of  1916.5  or  19165. 
Since  the  characteristic  is  2,  we  have  x  =  191.65. 

Ex.  4.  Given  logx  =  1.03720,  to  find  x  to  six  places. 

When  the  mantissa  is  less  than  .04175,  we  use  pages  20  and  21. 

The  next  less  mantissa  is  .03719,  mantissa  of  10894. 


viii  EXPLANATION  OF  TABLES 

The  tabular  difference  is  4 ;  hence  the  correction  is  ^  of  1,  or  .3. 

Hence  X  =  0.108943. 

If  only  five  places  were  required,  interpolation  would  be  unnecessary. 

Ex.  5.  Given  logx  =  -  1.23457,  to  find  x. 

Here  log  x  is  not  in  the  type  form  ;  —  1  is  not  the  characteristic  nor  is  —  .23457 
the  mantissa.  To  put  log  x  in  the  type  form  we  add  0  in  the  form  —  1  +  1 ;  we 
thus  obtain 

logx  =  -  2  +  (1  -  .23457)  =  2.76543,  or  8.76543  -  10. 
.-.  X  =  0.058268. 

Ex.  6.  Find  the  value  of  x  in  each  of  the  following  equations  : 

log  X  =  1.96557 ;  log  x  =  1.83159  ;  log  x  =  3.49101  ; 
log  X  =  1.37665 ;  log  x  =  2.54153  ;  log  x  =  2.87972. 

For  the  answers  see  example  4  in  §  2. 

Ex.  7.  Given  x  =  432/5271,  to  find  x  by  logarithms. 
Here  log  x  =  log  432  -  log  5271. 

log  432  =  2.63548  =  12.63548  -  10 
log  5271=  3.72189 

.-.  logx=  8.91359-10 

.-.  X  =  0.08196. 

Observe  that  before  we  subtract  we  write  the  characteristic  2  in  the  form 
12  —  10,  and  thus  make  the  positive  part  of  the  minuend  greater  than  the 
positive  part  of  the  subtrahend. 

Ex.  8.  Given  x  =  \/32.17  x  .00271,  to  find  x  by  logarithms. 
Here  log  x  =  (log  32. 17  +  log  .00271)/4. 

log  32.17  =  1.50745 
log  .00271  =  3.43297 
.-.  logx  =  2.94042/4 

=  (38.94042 -40)/4 
=  9.73511-10,  or  L  73511. 
.-.  X  =  0.54339. 

Note  that  before  dividing  by  4  we  write  the  characteristic  —  2  in  the  form 
38  —  40,  so  that  the  negative  part,  —  40,  when  divided  by  4  gives  —  10  as  a 
quotient. 

Table  II 

4.  This  table  contains  the  values  and  logarithms  of  some  impor- 
tant constants  and  their  combinations  which  most  frequently  occur. 
The  table  needs  no  explanation. 


EXPLANATION  OF  TABLE  IH  ix 


Table  III 

5.  This  table  contains  the  logarithms  of  the  sines,  cosines,  tan- 
gents, and  cotangents  of  angles  from  1°  to  89°  at  intervals  of  1'. 

When  the  angle  is  less  than  45°,  the  number  of  degrees  is  found 
at  the  top  of  the  page,  the  number  of  minutes  in  the  left-hand 
minute  column,  and  the  name  of  the  function  at  the  top  of  the 
column  of  mantissas.  When  the  angle  is  greater  than  45°,  the 
number  of  degrees  is  found  at  the  bottom  of  the  page,  the  number 
of  minutes  in  the  right-hand  minute  column,  and  the  name  of  the 
function  at  the  bottom  of  the  column  of*  mantissas. 

The  mantissa  is  in  the  same  row  as  the  number  of  minutes,  and 
the  characteristic  is  at  the  top  or  bottom  of  the  column  of  mantissas. 

The  characteristic  at  the  top  of  any  column  is  usually  the  same 
as  that  at  the  bottom  ;  the  only  exceptions  are  found  on  pages  26 
and  45,  where  the  characteristic  at  the  top  of  the  column  is  to  be 
taken  with  any  mantissa  above  the  bar,  and  the  characteristic  at  the 
bottom,  is  to  be  taken  with  any  mantissa  below  the  bar. 

6.  To  find  the  logarithm  of  the  sine,  cosine,  tangent,  or  cotangent 
of  a  given  angle. 

The  following  rules  for  characteristics  should  be  used  when 
applicable. 

(a)  The  characteristic  of  the  sine  of  an  angle  between  6°  and  90°,  or  of  the  cosine 
of  an  angle  between  0°  and  84°,  is  9  —  10. 

For  sin  6°  =  cos  84°  >  0.1,  sin  90°  =  cos  0°  =  1,  and  the  characteristic 
of  a  number  between  0.1  and  1  is  —  1,  or  9  —  10. 

(b)  The  characteristic  of  the  tangent  of  an  angle  between  6°  and  45°,  or  of  the 
cotangent  of  an  angle  between  45°  and  84°,  is  9  —  10. 

For  tan  6°  =  cot  84°  >  0.1,  tan  45°  =  cot  45°  =  1,  and  the  characteristic 
of  a  number  between  0.1  and  1  is  —  1,  or  9  —  10. 

(c)  The  characteristic  of  the  tangent  of  an  angle  between  45°  and  84°,  or  of 
the  cotangent  of  an  angle  between  6°  and  45°,  is  0. 

For  tan  45°  =  cot  45°  =  1,  tan  84°  =  cot  6°  <  10,  and  the  characteristic 
of  a  number  between  1  and  10  is  0. 
By  the  rules  above  what  is  the  characteristic  of  sin  7°  ?   sin  88°  ?   cos  4°  ? 
cos  83°?  tan6°?  tan  44°?  cot  46°?  cot  83°?  tan  47°?  cot7°?  tan  78°?  cot  41°? 
Ex.  1.  Find  log  sin  35°  42',  i.e.,  the  logarithm  of  the  sine  of  35°  42'. 
By  (a),  the  characteristic  is  9  —  10.    On  page  41,  under  35°,  in  the  mantissa 
column  headed  "log  sin  "  and  in  the  row  42'  we  find  the  mantissa  .76607.    Hence 
log  sin  35°  42'  =  9.76607  -  10. 

Note.     For  an  explanation  of  the  marginal  tabs  of  Table  III,  see  §  11. 


X  EXPLANATION  OF   TABLES 

Ex.  2.  Verify  each  of  the  following  identities  : 

log  tan  41°  32'  =  9.94732  -  10  ;         log  cos  29°  18'  =  9.94055  -  10  ; 
log  sin  68°  21'  =  9.96823  -  10  ;         log  cot  28°  35'  =  0.26373  ; 
log  tan  88°  35'  =  1.60677;  log  cos  61°  27'  =  9.67936  -  10 

Ex.  3.  Find  log  tan  32°  24'  33". 

To  interpolate  for  seconds,  we  assume  that  any  S7nall  increase  in  an  angle  is 
proportional  to  the  corresponding  increase  or  decrease  in  the  logarithm  of  any 
function  of  the  angle. 

log  tan  32°  24'  =  9.80251  -  10. 

The  tabular  difference  for  1',  or  60",  is  28  points. 

Hence,  if  an  increase  of  60"  in  the  angle  causes  an  increase  of  28  points  in 
the  mantissa,  an  increase  of  33"  in  the  angle  will  cause  an  increase  of  33/60  of 
28,  or  15,  points  in  the  mantissa. 

.-.  log  tan  32°  24'  33"  =  9.80266  -  10. 

Ex.  4.  Find  log  tan  81°  32'  14". 

logtan  81°  32' =  0.82723. 

The  tabular  difference  for  60"  is  87  points. 

Hence  the  correction  for  14"  is  ^^  of  87,  or  20,  points. 

.-.  log  tan  81°  32'  14"  =  0.82743. 

Ex.  5.  Find  log  cos  38°  25'  17". 

log  cos  38°  25'  =  9.89405  -  10. 

The  tabular  difference  for  60"  is  10  points. 

Hence  the  correction  for  17"  is  ^^  of  10,  or  3,  points. 

Since  the  cosine   decreases  as  the  angle  increases,  this  correction  is  to  be 

subtracted. 

.-.  log  cos  38°  25'  17"  =  9.89402  -  10. 

Ex.  6.  Find  log  cot  84°  38'  13". 

log  cot  84°  38'  =  8.97285  -  10. 

Here  we  take  the  characteristic  at  the  top  of  the  page,  since  the  mantissa  is 
above  the  bar. 

The  tabular  difference  for  60"  is  135  points. 

Hence  the  correction  for  13"  is  J§  of  135,  or  29,  points. 

.-.  log  cot  84°  38'  13"  =  9.97256  -  10. 

It  must  be  kept  in  mind  that  when  the  angle  increases  the  cosine 
or  the  cotangent  decreases;  hence  the  correction  for  seconds  must 
be  subtracted  in  finding  the  logarithm  of  the  cosine  or  cotangent  of 
an  angle. 

If  an  angle  is  less  than  2°  or  greater  than  88°,  and  involves  seconds, 
consult  Table  IV. 


EXPLANATION  OF  TABLE  III  xi 

Ex.  7.  Verify  each  of  the  following  identities  : 
log  sin  34°  9'  17''  =  9.74929  -  10  ;  log  sin  61°  56'  43"  =  9.94671  -  10  ; 
log  tan  42°  16'  41"  =  9.95867  -  10  ;  log  tan  78°  19'  31"  =  0.68481  ; 
log  cos  26°  17'  13"  =  9.95260  -  10  ;  log  cos  81°  51'  35"  =  9.15106  -  10  ; 
log  cot  25°  50' 20"  =  0.31492  ;  log  cot  84°  25'  30"  =  8.98950  -  10. 

7.  To  find  the  value  of  an  angle  when  the  logarithm  of  its  sine, 
cosine,  tangent,  or  cotangent  is  given. 

Ex.  1.  Given  log  sin  A  =  9.48213  -  10,  to  find  a  value  of  A. 
On  page  32,  in  column  headed  "log sin,"  under  17°,  in  row  40',  we  Snd  the 
given  mantissa,  the  given  characteristic  being  at  the  top  of  this  column. 

.-.  A  =  17°  40'. 

Observe  that  when  the  characteristic  of  sin  A  or  cos  ^  is  —  1,  a 
mantissa  less  than  .84949  is  in  a  column  headed  "  log  sin,"  while  a 
mantissa  greater  than  .84949  is  in  a  column  footed  "  log  sin." 

When  the  characteristic  of  tan  A  or  cot  A  is  —  1,  the  mantissa 
is  in  a  column  headed  "  log  tan  "  ;  when  the  characteristic  is  0,  the 
mantissa  is  in  a  column  footed  "  log  tan." 

When  the  characteristic  of  any  function  is  + 1  or  —  2,  the  angle 
is  less  than  6°  or  greater  than  84°  ;  hence  we  consult  one  of  ihe 
first  three  pages  of  the  table. 

Ex.  2.  Find  the  value  of  A  in  each  of  the  following  equations : 

log  sin  A  =  9.96823  -  10  ;         log  tan  A  =  9.94732  -  10  ; 
log  cos  A  =  9.94055  -  10  ;        log  cot  A  =  0.26373. 

For  the  answers  see  example  2  in  §  6. 

Ex.  3.  Given  log  sin  A  -  9.93422  -  10,  to  find  the  value  of  A. 

The  given  mantissa  is  not  found  in  the  table. 

The  next  less  mantissa  is  .93420,  mantissa  of  sin  59°  15'. 

The  tabular  difference  for  60"  is  7  points. 

The  given  mantissa  exceeds  the  next  less  by  2  points. 

Hence  the  correction  is  f  of  60",  or  17". 

.-.  A  =  59°  15'  17". 

Ex.  4.  Given  log  tan  ^  =  0.46940,  to  find  the  value  of  A. 
The  next  less  mantissa  is  .46922,  mantissa  of  tan  71°  15'. 
The  tabular  difference  for  60"  is  41  points. 
The  given  mantissa  exceeds  the  next  less  by  18  points. 
Hence  the  correction  is  ^f  of  60",  or  26". 

.-.  A  =  71°  15'  26". 

Ex.  5.  Given  log  cos  A  =  9.56871  —  10,  to  find  the  value  of  A. 
The  next  less  mantissa  is  .56854,  mantissa  of  cos  68°  16'. 
The  tabular  difference  for  60"  is  32  points. 


xii  EXPLANATION  OF  TABLES 

The  given  mantissa  exceeds  the  next  less  by  17  points. 
Hence  the  correction  is  ^^  of  60",  or  32''. 

Since  the  angle  decreases  when  the  cosine  increases,  we  subtract  this  correc- 
tion from  68°  16'  and  obtain 

A  =  68°  15'  28". 

Ex.  6.  Find  the  value  of  A  in  each  of  the  following  equations  : 


log  sin  ^  =  9.74929-  10 
log  tan  J.  =  9.95867  -  10 
log  cos  ^  =9.95260-10 
log  cot  A  =  0.31492  ;  log  cot  A  =  8.98950  -  10. 

For  the  answers  see  example  7  in  §  6. 


log  sin  J.  =  9.94571  -  10; 

log  tan  ^  =0.68481  ; 

log  cos  ^  =9.15106  -  10; 


Table  IV 

S.  The  first  page  of  this  table  contains  the  logarithms  of  the 
sines  of  angles  from  0°  to  0°  3'  at  intervals  of  1",  or  the  logarithms 
of  cosines  of  angles  from  89°  57'  to  90°.  Since  within  the  limits  of 
0°  and  3',  to  five  places  of  decimals,  log  tan  A  =  log  sin  A,  and  within 
the  limits  of  89°  57'  and  90°  log  cot  A  =  log  cos  A,  any  log  sin  on 
this  page  can  be  taken  as  log  tan,  and  any  log  cos  as  log  cot. 

E.g.,  log  tan    0°    1'  52"  =  log  sin    0°     1'  52"  =  6.73479  -  10  ; 
and         log  cot  89°  58'  37"  =  log  cos  89°  58'  37"  =  6.60465  -  10. 

The  other  pages  of  this  table  contain  the  logarithms  of  the  sines, 
cosines,  and  tangents  of  angles  from  3'  to  2°  at  intervals  of  10"; 
also  the  logarithms  of  the  sines,  cosines,  and  cotangents  of  angles 
from  88°  to  89°  57'  at  intervals  of  10". 

For  the  explanation  of  the  marginal  tabs  see  §  12. 

Ex.         Find  log  sin  0°  50'  25". 

log  sin  0°  50'  20"  =  8.16557  -  10. 
The  tabular  difference  for  10"  is  143  points. 
Hence  the  correction  for  5"  is  j%  of  143,  or  72,  points. 

.-.  log  sin  0°  50'  25"  =  8.16629  -  10. 
Similarly  log  cos  1°  48'  35"  =  9.99978  -  10. 

Also  log  tan  0°  46'  32"  =  8.13152  -  10.        log  cot  88°  32'  43"  =  8.40475  -  10. 

Any  logarithmic  tangent  or  cotangent  found  in  this. table  is  nega- 
tive. Hence  when  log  tan  A  or  log  cot  A  is  positive,  we  use  the 
relation  log  cot  A  =  —  log  tan  A  before  consulting  the  table. 

E.g. ,  log  cot  0°  2'  15"  =  0  -  log  tan  0°  2'  15" 

=  (10  -  10)  -  (6.81591  -  10)  =  3.18409. 
Again,  if  log  tan  A  =  2.35063, 

log  cot  ^  =  10  -  2.35063  -  10  =  7.64937  -  10. 
.-.^  =  89°  44' 40". 


EXPLANATION  OF  TABS  xiii 

Table  V 

9.  This  four-place  table  contains  the  natural  sines,  cosines,  tan- 
gents, and  cotangents  of  angles  from  0°  to  90°  at  intervals  of  1'. 

For  the  explanation  of  the  marginal  tabs  see  §  13.    ' 

Ex.  1,    Verify  each  of  the  following  identities  : 

sin  27°  42' =  0.4648  ;   tan  72°  21' =  3.1429  ;   sin  22°  3' 22'' =  0.3755  •, 
cos  68°  43'  =  0.3630  ;   cot  82°  28'  =  0.1322  ;  tan  60°  4'  38"  =  1.7375. 

Ex.  2.    Find  the  value  of  A  in  each  of  the  following  equations  : 
sin  ^  1=0.4648  ;         tan  ^  =  3.1429;         sin  ^  =  0.3755; 
cos  A  =  0.3630  ;         cot  A  =  0. 1322  ;        tan  ^  =  1.7375. 

Ex.  3.  The  bearing  of  a  course  is  N.  25°  42'  E.,  and  its  length  is  9.32  chains  ; 
find  its  latitude  and  departure  to  two  decimal  places. 

Latitude  ==  9.32  sin  25°  42'  =  9.32  x  0.434  =  4.04  chains. 
Departure  =  9.32  cos  25°  42'  =  9.32  x  0.901  =  8.40  chains. 

Explanation  of  Marginal  Tabs 

10.  Table  I.  The  pupil  should  place  his  book  of  tables  on  his 
desk  at  his  left,  and  in  manipulating  them  use  only  his  left  hand. 
If  he  opens  the  tables  with  the  projecting  tab  B,  all  the  marginal 
tabs  of  Table  I  can  be  seen  in  the  left-hand  margin.  Using  the 
projecting  tab  A,  he  puts  his  forefinger  under  the  first  pages  of  the 
table,  and  placing  his  thmPxb  on  any  marginal  tab,  as  tab  5,  he  turns 
to  the  right  the  leaves  not  held  between  his  thumb  and  finger,  thus 
opening  the  table  at  the  pages  marked  by  the  marginal  tab  5. 
When  thus  opened  it  is  found  that  the  first  figure  on  the  marginal 
ta,b  used  is  the  first  figure  of  every  number  found  on  the  pages 
opened,  that  the  mantissa  on  this  tab  is  the  least  mantissa  on  these 
pages,  and  that  the  greatest  mantissa  on  these  pages  is  a  little 
greater  than  the  mantissa  on  the  next  tab  below. 

Hence,  to  find  the  pages  needed  when  the  number  is  given,  use 
the  tab  which  has  on  it  the  first  figure  of  the  given  number. 

To  find  the  pages  needed  when  the  logarithm  is  given,  use  the  tab 
which  has  on  it  the  matitissa  next  less  than  the  given  one. 

11.  Table  III.  Open  the  book  of  tables  with  tab  C,  so  that  all 
the  marginal  tabs  of  Table  III  can  be  seen  in  the  left-hand  margin. 
Opening  this  table  with  any  marginal  tab,  as  tab  17°  —  20°,  we  find 
that  the  number  of  degrees  at  the  top  of  this  tab  are  those  at  the 
tops  of  the  pages  opened,  and  that  the  numbers  of  degrees  at  the 


xiv  EXPLANATION  OF  TABLES 

bottom  of  tnis  tab  are  those  at  the  bottoms  of  these  pages.  The 
first  mantissa  on  this  tab  is  the  least  mantissa  on  these  pages,  in 
the  columns  headed  "  log  sin,"  and  the  greatest  mantissa  in  these 
columns  is  the  first  mantissa  on  the  next  tab  below.  The  second 
mantissa  on  this  tab  is  the  least  mantissa  on  these  pages,  in  the 
columns  headed  ^'  log  tan,"  and  the  greatest  mantissa  in  these  col- 
umns is  the  second  mantissa  on  the  next  tab  below. 

The  last  mantissa  on  this  tab  is  the  least  mantissa  on  these 
pages,  in  the  columns /oo^ec^  "log  sin,"  and  the  greatest  mantissa  in 
these  columns  is  the  last  mantissa  on  the  next  tab  above. 

The  mantissa  next  to  the  last  is  the  least  mantissa  on  these  pages 
in  the  columns  footed  '<  log  tan,"  and  the  greatest  mantissa  in  these 
columns  is  the  corresponding  mantissa  on  the  next  tab  above.    Hence: 

To  find  the  pages  needed  when  the  angle  is  given,  use  the  tab  on 
which  the  number  of  degrees  is  written  or  included. 

To  find  the  pages  needed  when  log  sin  or  log  cos  is  given,  and 
the  characteristic  is  9  —  10,  use  the  tab  whose  first  or  last  mantissa 
is  the  next  less  than  the  given  one. 

To  find  the  pages  needed  when  log  tan  or  log  cot  is  given : 

When  the  characteristic  is  9  —  10,  use  the  tab  whose  second  man- 
tissa is  the  next  less  than  the  given  one. 

When  the  characteristic  is  0,  use  the  tab  whose  mantissa  next  to 
the  last  is  the  next  less  than  the  given  one. 

When  the  characteristic  of  any  function  is  —  2  or  +  1,  look  for 
the  logarithm  on  one  of  the  first  three  pages  of  the  table. 

On  tab  41°-44°  observe  that  the  last  mantissa  is  the  greatest  in 
the  columns  headed  ''log  sin,"  as  well  as  the  least  in  the  columns 
footed  "log  sin";  and  that  the  mantissa  next  to  the  last  is  the 
greatest  logarithm  in  the  columns  headed  "  log  tan,"  as  well  as  the 
least  in  the  columns  footed  "  log  tan." 

Where  no  characteristic  is  written  before  a  mantissa  on  any  tab, 
1  is  understood  with  the  first,  second,  or  fourth  mantissa,  and  0 
with  the  third. 

12.  Table  IV.  To  open  the  tables,  use  the  projecting  tab  D.  The 
first,  the  second,  and  the  last  logarithm  on  any  marginal  tab  have 
the  same  meaning  and  use  respectively  as  the  first,  the  second,  and 
the  last  logarithm  on  a  tab  in  Table  III. 

Since  the  logarithmic  tangents  of  angles  between  88°  and  90°  are 
not  recorded  in  this  table,  its  tabs  have  no  logarithm  corresponding 
to  the  third  logarithm  on  a  tab  in  Table  III. 


EXPLANATION  OF  TABS 


XV 


13.  Table  V.    To  open  t,he  tables,  use  the  projecting  tab  E. 

To  find  the  pages  needed  when  the  angle  is  given,  use  the  mar- 
ginal tab  on  which  the  name  of  the  required  function  is  written 
and  the  given  number  of  degrees  is  written  or  included. 

To  find  the  pages  needed  when  a  function  is  given,  use  a  tab  on 
which  the  name  of  the  given  function  is  written  and  on  which  the 
first  or  the  last  function  is  the  next  less  than  the  given  one. 

If  this  next  less  function  is  the  first  on  the  tab,  the  given  func- 
tion will  be  found  in  a  column  headed  "sin  "  or  "  tan  "  ;  if  it  is  the 
last  on  the  tab,  the  given  function  will  be  found  in  a  column  footed 
"sin"  or  "tan." 


14.  Table  VI.  This  table  is  to  be  used  when  greater  accuracy- 
is  required  than  can  be  secured  by  interpolation  in  Table  IV. 

In  it         a  =  the  number  of  seconds  in  an  angle  less  than  2°  2', 

S  =  log  (sin  a" /a)  =  log  sin  a"  —  log  «r,  (1) 

T  =  log  (tan  a" /a)  =  log  tan  a"  —  log  a.  (2) 

From  (1),  log  sin  a"  can  be  obtained  from  S  and  a,  or  a  can  be 
found  from  S  and  log  sin  a".  From  (2),  log  tan  a"  can  be  obtained 
from  T  and  a,  or  a  can  be  found  from  T  and  log  tan  a". 


Ex.  1.    Find  log  sin  0°  42'  13". 
0°  42'  13"  =  2533"  =  a", 
.-.log  a  =  3.40364 

S  =  4.68556  -  10 
.-.  log  sin  a"  =  8.08920  -  10 

Ex.  3.    Find  log  tan  0°  58'  32.7' 

0°  58' 32.7"  =  3512.7"  =  a". 

log  a:  =  3.54564 

r=  4.68562  -  10 
.-.  log  tan  a"  =  8.23126  -  10 


Find  A  when  there  is  given  : 

Ex.  5.    logsin^  =  6.67237- 

10. 

Here  ^  <  2°  ; 

hence  we  put 

log  sin  <3:" 

=  6.67237  -  10 

S 

=  4.68557  -  10 

.'.  log  a 

=  1.98680 

.-.  a" 

=  97.006" 
=  r  37.006". 

Ex.  2.    Find  log  cos  88°  18' 21.2". 
cos  88°  18'  21.2"  =  sin  1°  41'  38.8". 
1°41'38.8"  =  6098.8"  =  a", 
.-.log  a  =  3.78525 

S  =  4.68551  -  10 
.-.  log  cos  88°  18'  21.2"  =  8.47076  -  10 

Ex.  4.    Find  log  tan  89°  13'  34.22". 
cot  89°  13'  34.22"  =  tan  46'  25.78". 
46'  25.78"  =  2785.78"  =  a". 
.-.  log  a  =  3.44495 

T=  4.68560-  10 
.-.  log  cot  89°  13'  34.22"  =  8. 13055  -  10 
.-.log  tan  89°  13' 34.22"  =  1.86945. 


Ex.  6.    log  tan  A  =  2.35427. 
Let       log  tan  a"  =  log  cot  A  ;  then 
log  tan  a"  =  7.64573-10 
r=  4.68558  -  10 
.-.  log  a  =  2.96015 
.-.  a"  =  912.32"  =  15'  12.32". 
.-.  ^  =  90°  -  a"  =  89°  44'  47.68". 


:  :  \'^\  V\. 

; 

•••  :•* 

TABLE  I    :         i    ^;r 

•  *  •  •  *i 

*:  • ;  i .;. 

•  ••  ••    • 

FIVE-PLACE  MANTISSAS 

OF  THE 

commojn"  logarithms 

OF  THE 

ENTIRE  NUMBERS 

From  1  to  11000 

1-100 

N 

M 

N 

M 

N 

M 

N 

M 

N 

'     M 

1 

.00  000 

21 

.32  222 

41 

.61  278 

61 

.78  533 

81 

.90  849 

2 

30103 

22 

34  242 

42 

62  325 

62 

79  239 

82 

91381 

3 

47  712 

23 

36  173 

43 

63  347 

63 

79  934 

83 

91908 

4 

60  206 

24 

38  021 

44 

64  345 

64 

80  618 

84 

92  428 

5 

69  897 

25 

39  794 

45 

65  321 

65 

81291 

85 

92  942 

6 

.77  815 

26 

.41  497 

46 

.66  276 

66 

.81  954 

86 

.93  450 

7 

84  510 

27 

43  136 

47 

67  210 

67 

82  607 

87 

93  952 

8 

90  309 

28 

44  716 

48 

68  124 

68 

83  251 

88 

94  448 

9 

95  424 

29 

46  240 

49 

69  020 

69 

83  885 

89 

94  939 

10 

00  000 

30 

47  712  . 

50 

69  897 

70 

84  510 

90 

95  424 

11 

.04  139 

31 

.49136 

51 

.70  757 

71 

.85  126 

91 

.95  904 

12 

07  918 

32 

50  515 

52 

71600 

72 

85  733 

92 

96  379 

13 

11394 

33 

51851 

53 

72  428 

73 

86  332 

93 

96  848 

14 

14  613 

34 

53  148 

54 

73  239 

74 

86  923 

94 

97  313 

15 

17  609 

35 

54  407 

55 

74  036 

75 

87  506 

95 

97  772 

16 

.20  412 

36 

.55  630 

56 

.74  819 

76 

.88  081 

96 

.98  227 

17 

23  045 

37 

56  820 

57 

75  587 

77 

88  649 

97 

98  677 

18 

25  527 

38 

57  978 

58 

76  343 

78 

89  209 

98 

99  123 

19 

27  875 

39 

59  106 

59 

77  085 

79 

89  763 

99 

99  564 

20 

30103 

40 

60  206 

60 

77  815 

80 

90  309 

100 

00  000 

1000-1500 


N^ 

.^^.^^      ^i^^^ :» ;  ;  3      4 

5    6    7    8    9 

Dif. 

100 

.QC  QGG  ,0Q  a43  .00  087  .00  130  .00  173 

.00  217  .00  260  .00  303  .00  346  .00  389 

40  39 

1(51^ 

^  U3^;  :475:   £13   561   604 

647   689   732   775   817 

4   4 

l02 

^  ^^60   903^   945   988.01030 

01  072  01  115  01  157  01  199  01  242 

8   8 

103 

01  284  01  326  01  368  01  410   452 

494   536   578   620   662 

12  12 

104 

703   745   787   828   870 

912   953   995  02  036  02  078 

16  16 

105 

.02  119  .02  160  .02  202  .02  243  .02  284 

.02  325  .02  366 .02  407  .02  449  .02  490 

20  20 

106 

531   572   612   653   694 

735   776   816   857   898 

24  23 

107 

938   979  03  019  03  060  03  100 

03  141  03  181  03  222  03  262  03  302 

28  27 

108 

03  342  03  383   423   463   503 

543   583   623   663   703 

32  31 

109 

743   782   822   862   902 

941   981  04  021  04  060  04  100 

36.  35 

110 

.04  139  .04  179  .04  218  .04  258  .04  297 

.04  336  .04  376  .04  415  .04  454  .04  493 

38  86 

111 

532   571   610   650   689 

727   766   805   844   883 

4   4 

112 

922   961   999  05  038  05  077 

05  115  05  154  05  192  05  231  05  269 

8   7 

113 

:  05  308  05  346  05  385   423   461 

500   538   576   614   652 

11  11 

114 

690   729   767   805   843 

881   918   956   994  06  032 

15  14 

115 

.06  070 .06  108  .06  145  .06  183  .06  221 

.06  258  .06  296  .06  333  .06  371 .06  408 

19  18 

116 

446   483   521   558   595 

633   670   707   744   781 

23  22 

117 

819   856   893   930   967 

07  004  07  041  07  078  07115  07151 

27  25 

118 

07  188  07  225  07  262  07  298  07  335 

372   408   445   482   518 

30  29 

119 

555   591   628   664   700 

737   773   809   846   882 

34  32 

120 

.07  918  .07  954  .07  990  .08  027  .08  063 

.08  099  .08  135  .08  171 .08  207  .08  243 

34  33 

121 

08  279  08  314  08  350   386   422 

458   493   529   565   600 

3   3 

122 

636   672   707   743   778 

814   849   884   920   955 

7   7 

123 

991  09  026  09  061  09  096  09  132 

09  167  09  202  09  237  09  272  09  307 

10  10 

124 

09  342   377   412   447   482 

517   552   587   621   656 

14  13 

125 

.09  691 .09  726 .09  760  .09  795  .09  830 

.09  864  .09  899 .09  934  .09  968  .10  003 

17  17 

126 

10  037  10  072  10106  10140  10175 

10  209  10  243  10  278  10  312   346 

20  20 

127 

380   415   449   483   517 

551   585   619   653   687 

24  23 

128 

721   755   789   823   857 

890   924   958   992  11025 

27  26 

129 

11059  11093  11126  11160  11193 

11227  11261  11294  11327   361 

31  30 

130 

.11  394  .11  428  .11  461  .11  494  .11  528 

.11  561 .11  594  .11  628  .11  661 .11  694 

32  31 

131 

727   760   793   826   860 

893   926   959   992  12  024 

3   3 

132 

12  057  12  090  12  123  12  156  12  189 

12  222  12  254  12  287  12  320   352 

6   6 

133 

385   418   450   483   516 

548   581   613   646   678 

10   9 

134 

710   743   775   808   840 

872   905   937   969  13  001 

13  12 

135 

.13  033  .13  066  .13  098  .13  130  .13  162 

.13  194  .13  226  .13  258  .13  290  .13  322 

16  16 

136 

354   386   418   450   481 

513   545   577   609   640 

19  19 

137 

672   704   735   767   799 

830   862   893   925   956 

22  22 

138 

988  14  019  14  051  14  082  14  1,14 

14  145  14  176  14  208  14  239  14  270 

26  25 

139 

14  301   333   364   395   426 

457   489   520   551   582 

29  28 

140 

.14  613  .14  644  .14  675  .14  706 .14  737 

.14  768  .14  799  .14  829  .14  860  .14  891 

30  29 

141 

922   953   983  15  014  15  045 

15  076  15  106  15  137  15  168  15  198 

3   3 

142 

15  229  15  259  15  290   320   351 

381   412   442   473   503 

6   6 

143 

534   564   594   625   655 

685   715   746   776   806 

9   9 

144 

836   866   897   927   957 

987  16  017  16  047  16  077  16107 

12  12 

145 

.16  137  .16  167  .16  197  .16  227  .16  256 

.16  286  .16  316  .16  346  .16  376  .16  406 

15.  15 

146 

435   465   495   524   554 

584   613   643   673   702 

18  17 

147 

732   761   791   820   850 

879   909   938   967   997 

21  20 

148 

17  026  17  056  17  085  17114  17143 

17173  17  202  17  231  17  260  17  289 

24  23 

149 

319   348   377   406   435 

464   493   522   551   580 

27  26 

150 

N 

.17  609  .17  638  .17  667  .17  696  .17  725 

.17  754  .17  782  .17  811 .17  840  .17  869 

0    12    3    4 

5    6    7    8    9 

.00  000 -.17  869 


1500 

-2000 

3 

N 
150 

0    12    3    4 

5    6    7    8    9 

Dif. 

.17  609  .17  638  .17  667  .17  696  .17  725 

.17  754  .17  782  .17  811 .17  840  .17  869 

29  27 

151 

898   926   955   984  18  013 

18  041  18  070  18  099  18  127  18156 

3   3 

152 

18  184'  18  213  18  241  18  270   298 

327   355   384   412   441 

6   5 

153 

469   498   526   554   583 

611   639   667   696   724 

9   8 

154 

752   780   808   837   865 

893   921   949   977  19  005 

12  11 

155 

.19  033  .19  061 .19  089  .19  117  .19  145 

.19  173  .19  201  .19  229  .19  257  A9  285 

15  14 

156 

312   340   368   396   424 

451   479   507   t35  '  562 

17  16 

157 

590   618   645   673   700 

728   756   783   811   838 

20  19 

158 

866   893   921   948   976 

20  003  20  030  20  058  20  085  20112 

23  22 

159 

20  140  20  167  20  194  20  222  20  249 

276   303   330   358   385 

26  24 

160 

.20  412  .20  439  .20  466  .20  493  .20  520 

.20  548  .20  575  .20  602  .20  629  .20  656 

26  25 

161 

683   710   737   763   790 

817   844   871   898   925 

3   3 

162 

952   978  21  005  21  032  21  059 

21  085  21  112  21  139  21  165  21  192 

5   5 

163 

21 219  21 245   272   299   325 

352   378   405   431   458 

8   8 

164 

484   511   537   564   590 

617   643   669   696   722 

10  10 

165 

.21  748  .21  775  .21  801  .21  827  .21  854 

.21  880  .21  906  .21  932  .21  958  .21  985 

13  13 

166 

22  011  22  037  22  063  22  089  22  115 

22  141  22  167  22  194  22  220  22  246 

16  15 

167 

272   298   324   350   376 

401   427   453   479   505 

18  18 

168 

531   557   583   608   634 

660   686   712   737   763 

21  20 

169 

789   814   840   866   891 

917   943   968   994  23  019 

23  23 

170 

.23  045  .23  070  .23  096  .23  121  .23  147 

.23  172  .23  198  .23  223  .23  249  .23  274 

25  24 

171 

300   325   350   376   401 

426   452   477   502   528 

3   2 

172 

553   578   603   629   654 

679   704   729   754   779 

5   5 

173 

805   830   855   880   905 

930   955   980  24  005  24  030 

8   7 

174 

24  055  24  080  24  105  24  130  24  155 

24  180  24  204  24  229   254   279 

10  10 

175 

.24  304  .24  329  .24  353  .24  378  .24  403 

.24  428  .24  452  .24  477  .24  502  .24  527 

13  12 

176 

551   576   601   625   650 

674   699   724   748   773 

15  14 

177 

797   822   8+6   871   895 

920   944   969   993  25  018 

18  17 

178 

25  042  25  066  25  091  25  115  25  139 

25  164  25  188  25  212  25  237   261 

20  19 

179 

285   310   334   358   382 

406   431   455   479   503 

23  22 

180 

.25  527  .25  551  .25  575  .25  600  .25  624 

.25  648  .25  672  .25  696  .25  720 .25  744 

24  23 

181 

768   792   816   840   864 

888   912   935   959   983 

2   2 

182 

26  007  26  031  26  055  26  079  26  102 

26126  26  150  26  174  26198  26  221* 

5   5 

183 

245   269   293   316   340 

364   387   411   435   458 

7   7 

184 

482   505   529   553   576 

600   623   647   670   694 

10   9 

185 

.26  717  .26  741 .26  764  .26  788  .26  811 

.26  834  .26  858  .26  881  .26  905  .26  928 

12  12 

186 

951   975   998  27  021  27  045 

27  068  27  091  27  114  27  138  27  161 

14  14 

187 

27  184  27  207  27  231   254   277 

300   323   346   370   393 

17  16 

188 

416   439   462   485   508 

531    554   577   600   623 

19  18 

189 

646   669   692   715   738 

761    784   807   830   852 

22  21 

190 

.27  875  .27  898  .27  921 .27  944  .27  967 

.27  989  .28  012  .28  035  .28  058  .28  081 

22  21 

191 

28  103  28  126  28  149  28  171  28  194 

28  217   240   262   285   307 

2   2 

192 

330   353   375   398   421 

443   466   488   511   533 

4   4 

193 

-  556   578   601   623   646 

668   691   713   735   758 

7   6 

780   80a   825   847   870 

892   914   937   959   981 

9   8 

195 

.29  003  .29  026  .29  048  .29  070  .29  092 

.29  115  .29  137  .29  159  .29  181  .29  203 

11  11 

196 

226   248   270   292   314 

336   358   380   403   425 

13  13 

197 

447   469  •  491   513   535 

557   579   601   623   645 

15  15 

198 

667   688   710   732   754 

776   798   820   842   863 

18  17 

199 

885   907   929   951   973 

994  30  016  30  038  30  060  30  081 

20  19 

200 

N 

.30  103  .30  125  .30  146  .30  168  .30  190 

.30  211 .30  233  .30  255  .30  276  .30  298 

0    12    3    4 

5    6    7    8    9 

17  609 -.30  298 


2000-2500 


N 
200 

0     12    3    4 

5    6    7    8    9 

Dif. 
21 

.30  103  .30  125  .30  146  .30  168  .30  190 

.30  211  .30  233  .30  255  .30  276  .30  298 

201 

320    341    363    384    406 

428    449    471    492    514 

2 

202 

535    557    578    600    621 

643    664    685    707    728 

4 

203 

750    771    792    814    835 

856    878    899   920   942 

6 

204 

963    984  31006  31027  31048 

31069  31091  31112  31133  31154 

8 

205 

.31 175  .31  197  .31  218  .31  239  .31  260 

.31  281  .31  302  .31  323  .31  345  .31  366 

11 

206 

387    408    429    450    471 

492    513    534  .   555    576 

13 

207 

597    618    639    660    681 

702    723    744    765    785 

15 

208 

806    827    848    869    890 

911    931    952    973    994 

17 

209 

32  015  32  035  32  056  32  077  32  098 

32  118  32  139  32  160  32181  32  201 

19 

210 

.32  222  .32  243  .32  263  .32  284  .32  305 

.32  325  .32  346  .32  366  .32  387  .32  408 

20 

211 

428    449    4^9    490    510 

531    552    572    593    613 

2 

212 

634    654    675    695    715 

736   756    777    797   818 

4 

213- 

838    858    879    899    919 

940   960    980  33  001  33  021 

6 

214 

33  041  33  062  33  082  33  102  33  122 

33143  33  163  33  183    203    224 

8 

215 

.33  244  .33  264  .33  284  .33  304  .33  325 

.33  345  .33  365  .33  385  .33  405  .33  425 

10 

216 

445    465  .  486    506    526 

546    566    586    606    626 

12 

217 

646   666    686    706    726 

746    766    786    806    826 

14 

218 

846    866    885    905    925 

945    965    985  34  005  34  025 

16 

219 

34  044  34  064  34  084  34104  34  124 

34  143  34  163  34183    203    223 

18 

220 

.34  242  .34  262  .34  282  .34  301  .34  321 

.34  341  .34  361  .34  380  .34  400  .34  420 

19 

221 

439    459   479    498    518 

537    557    577   596   616 

2 

222 

635    655    674    694    713 

733    753    772   792    811 

4 

223 

830    850    869    889    908 

928    947    967    986  35  005 

6 

224 

35  025  35  044  35  064  35  083  35  102 

35  122  35  141  35  160  35  180    199 

8 

225 

.35  218  .35  238  .35  257  .35  276  .35  295 

.35  315  .35  334  .35  353  .35  372  .35  392 

10 

226 

411    430   449    468    488 

507    526    545    564    583 

11 

227 

603    622    641    660    679 

698    717    736    755    774 

13 

228 

793    813    832    851    870 

889    908    927    946    965 

15 

229 

984  36  003  36  021  36  040  36  059 

36  078  36  097  36  116  36135  36154 

17 

230 

.36  173  .36192  .36  211  .36  229  .36  248 

.36  267  .36  286  .36  305  .36  324  .36  342 

18 

231 

361    380    399    418    436 

455    474    493    511    530 

2 

232 

549    568    586    605    624 

642    661    680   698    717 

4 

233 

736    754    773    791    810 

829    847    866    884    903 

5 

234 

922    940    959    977    996 

37  014  37  033  37  051  37  070  37  088 

7 

235 

.37  107  .37  125  .37  144  .37  162  .37  181 

.37  199  .37  218  .37  236  .37  254  .37  273 

9 

236 

291    310    328    346    365 

383    401    420   438    457 

11 

237 

475    493    511    530    548 

566    585    603    621    639 

13 

238 

658    676    694    712    731 

749    767    XS5    803    822 

14 

239 

840    858    876    894    912 

931    949    967   985  38  003 

16 

240 

.38  021  .38  039  .38  057  .38  075  .38  093 

.38  112  .38  130  .38  148  .38  166  .38  184 

17 

241 

202    220    238    256    274 

292    310    328    346   364 

2 

242 

382    399    417    435    453 

471    489    507    525    543 

3 

243 

561    578    596    614    632 

650    668    686    703    '"1 

~5 

244 

739    757    775    792    810 

828    846    863    881    89. 

7 

245 

.38  917  .38  934  .38  952  .38  970  .38  987 

.39  005  .39  023  .39  041  .39  058  .39  076 

9 

246 

39  094  39  111  39129  39  146  39164 

182    199    217    235    252 

10 

247 

270    287    305    322    340 

358    375    393    410   428 

12 

248 

445    463    480    498   .515 

533    550    568    585    602 

14 

249 

620    637    655    672    690 

707    724   742    759   777 

15 

250 

N 

.39  794  .39  811  .39  829  .39  846  .39  863 

.39  881  .39  898  .39  915  .39  933  .39  950 

0     12    3    4 

5     6     7     8     9 

.30 103 -.39  950 


2500-3000 


N 
250 

0 

1 

2 

3    4 

5 

.39  881 

6     7 

8 

9 

Dif. 
18 

.39  794 

.39  811 

.39  829 

.39  846  .39  863 

.39  898  .39  915 

.39  933 

.39  950 

251 

967 

985 

40  002 

40  019  40  037 

40  054 

40  071  40088 

40  106 

40123 

2 

252 

40140 

40157 

175 

192    209 

226 

243    261 

278 

295 

4 

253 

312 

329 

346 

364    381 

398 

415    432 

449 

466 

5 

254 

483 

500 

518 

535    552 

569 

586   603 

620 

637 

7 

255 

.40  654 

.40  671 

.40  688 

.40  705  .40  722 

.40  739 

.40  756  .40  773 

.40  790 

.40  807 

9 

256 

824 

841 

858 

875    892 

909 

926    943 

960 

976 

11 

257 

993 

41010 

41027 

41044  41061 

41078 

41095  41111 

41128 

41145 

13 

258 

41162 

179 

196 

212    229 

246 

263    280 

296 

313 

14 

259 

330 

347 

363 

380    397 

414 

430   447 

464 

48] 

16 

260 

.41  497 

.41  514 

.41  531 

.41  547  .41  564 

.41  581 

.41  597  .41  614 

.41  631 

.41  647 

171 

261 

664 

681 

697 

714    731 

747 

764    780 

797 

814 

2; 

262 

830 

847 

863 

880    896 

913 

929    946 

963 

979 

3' 

^ 

263 

996 

42012 

42  029 

42  045  42  062 

42  078 

42  095  42  111 

42  127 

42  144 

5' 

264 

42160 

177 

193 

210    226 

243 

259    275 

292 

308 

7i 

265 

.42  325 

.42  341 

.42  357 

.42  374  .42  390 

.42  406 

.42  423  .42  439 

.42  455 

.42  472 

9 

266 

488 

504 

521 

537    553 

570 

586    602 

619 

635 

10 

267 

651 

667 

684 

700    716 

732 

749    765 

781 

797 

12 

268 

813 

830 

846 

862    878 

894 

911    927 

943 

959 

14 

269 

.  975 

991 

43  008 

43  024  43  040 

43  056 

43  072  43  088 

43  104 

43  120 

15 

270 

.43  136 

.43  152 

.43  169 

.43185  .43  201 

.43  217 

.43  233  .43  249 

.43  265 

.43  281 

16 

271 

297 

313 

329 

345    361 

377 

393    409 

425 

441 

2 

272 

457 

473 

489 

505    521 

537 

553    569 

584 

600 

3 

273 

616 

632 

648 

664    680 

696 

712    727 

743 

759 

5 

274 

775 

791 

807 

823    838 

854 

870   886 

902 

917 

6 

275 

.43  933 

.43  949 

.43  965 

.43  981  .43  996 

.44  012 

.44  028  .44  044 

.44  059 

.44  075 

8 

276 

44  091 

44  107 

44  122 

44  138  44154 

170 

185    201 

217 

232 

10 

277 

248 

.  264 

279 

295    311 

326 

342    358 

373 

389 

11 

278 

404 

420 

436 

451    467 

483 

498    514 

529 

545 

13 

279 

560 

576 

592 

607    623 

638 

654    669 

685 

700 

14 

280 

.44  716 

.44  731 

.44  747 

.44  762  .44  778 

.44  793 

.44  809  .44  824 

.44  840 

.44  855 

16 

281 

871 

886 

902 

917    932 

948 

963    979 

994 

45  010 

2 

282 

45  025 

45  040 

45  056 

4S071  45  086 

45  102 

45  117  45  133 

45  148 

163 

3 

283 

179 

194 

209 

225    240 

255 

271    286 

301 

317 

5 

284 

332 

347 

362 

378    393 

408 

423    439 

454 

469 

6 

285 

.45  484 

.45  500 

.45  515 

.45  530  .45  545 

.45  561 

.45  576  .45  591 

.45  606 

.45  621 

8 

286 

637 

652 

667 

682    697 

712 

728    743 

758 

773 

9 

287 

788 

803 

818 

834    849 

864 

879    894 

909 

92f 

11 

288 

939 

954 

969 

984-  46  000 

46  015 

46  030  46  045 

46  060 

46  075 

12 

289 

46  090 

46105 

46120 

46 135    150 

165 

180    195 

210 

225 

14 

290 

.46  240 

.46  255 

.46  270 

.46  285  .46  300 

.46  315 

.46  330  .46  345 

.46  359 

.46  374 

14 

291 

389 

404 

419 

434    449 

464 

479    494 

509 

523 

1 

292 

538 

553 

568 

583    598 

613 

627    642 

657 

672 

3 

293 

687 

702 

716 

731    746 

761 

776    790 

805 

820 

4 

294 

835 

850 

864 

879    894 

909 

923    938 

953 

967 

6 

295 

.46  982 

.46  997 

.47  012 

.47  026  .47  041 

.47  056 

.47  070  .47  085 

.47  100 

.47  114 

7 

296 

47  129 

47  144 

159 

173    188 

202 

217    232 

246 

261 

8 

297 

276 

290 

305 

319    334 

349 

363    378 

392 

407 

10 

298 

422 

436 

451 

465    480 

494 

509    524 

538 

553 

11 

299 

567 

582 

596 

611    625 

640 

654    669 

683 

698 

13 

300 

N 

.47  712 

.47  727 

.47  741 

.47  756  .47  770 

.47  784 

.47  799  .47  813 

.47  828 

.47  842 

0 

1 

2 

3    4 

5 

6     7 

8 

9 

.39  794 -.47  842 


3000-3500 


N 

0     12    3 

4 

5 

6     7    8    9 

Dif. 
15 

300 

.47  7l5  .47  727  .47  741  .47  756 

.47  770 

.47  784 

.47  799  .47  813  .47  828  .47  842 

301 

857    871    885    900 

914 

929 

943    958    972    986 

2 

302 

48  001  48  015  48  029  48  044 

48  058 

48  073 

48  087  48  101  48  116  48  130 

3 

303 

144    159    173    187 

202 

216 

230    244    259    273 

5 

304 

287    302    316    330 

344 

359 

373    387    401    416 

6 

305 

.48  430  .48  444  .48  458  .48  473 

.48  487 

.48  501 

.48  515  .48  530  .48  544  .48  558 

8 

306 

572    586    601    615 

629 

643 

657    671    686    700 

9 

307 

714    728    742    756 

770 

785 

799    813    827    841 

11 

308 

855    869    883    897 

911 

926 

940    954    968    982 

12 

309 

996  49  010  49  024  49  038 

49  052 

49  066 

49  080  49  094  49108  49  122 

14 

310 

.49  136  .49  150  .49  164  .49  178 

.49  192 

.49  206 

.49  220  .49  234  .49  248  .49  262 

14 

311 

276    290    304    318 

332 

346 

360    374    388    402 

1 

312 

415    429    443    457 

471 

485 

499    513    527    541 

3 

313 

554    568    582    596 

610 

624 

638    651    665    679 

4 

314 

693    707    721    734 

748 

762 

776    790   803   817 

6 

315 

.49  831  .49  845  .49  859  .49  872 

.49  886 

.49  900 

.49  914  .49  927  .49  941  .49  955 

7 

316 

969    982    996  50  010 

50  024 

50037 

50  051  50  065  50  079  50  092 

8 

317 

50106  50120  50  133    147 

161 

174 

188    202    215    229 

10 

318 

243    256   270    284 

297 

311 

325    338    352    365 

11 

319 

379    393    406    420 

433 

447 

461    474    488    501 

13 

320 

.50  515  .50  529  .50  542  .50  556 

.50  569 

.50  583 

.50  596  .50  610  .50  623  .50  637 

13 

321 

651    654    678    691 

705 

718 

732    745    759    772 

1 

322 

786    799    813    826 

840 

853 

866    880    893    907 

3 

323 

920    934    947    961 

974 

987 

61001  51014  51028  51041 

4 

324 

51055  51068  51081  51095 

51108 

51121 

135    148    162    175 

5 

325 

.51188  .51202  .51215  .51228 

.51242 

.51  255 

.51268  .51282  .51295  .51308 

7 

326 

322    335    348    362 

375 

388 

^02    415    428    441 

8 

327 

455    458    481    495 

508 

521 

534    548    561    574 

9 

328 

587    601    614    627 

640 

654 

667    680    693    706 

10 

329 

720   733    746    759 

772 

786 

799    812    825    838 

12 

330 

.51851  .51865  .51878  .51891 

.51904 

.51917 

.51930  .51943  .51957  .51970 

13 

331 

983    996  52  009  52  022 

52  035 

52  048 

52  061  52  075  52  088  52101 

1 

332 

52  114  52  127    140    153 

166 

179 

192    205    218    231' 

3 

333 

244    257    270    284 

297 

310 

323    336    349-   362 

4 

334 

375    388   401   414 

427 

440 

453    466    479    492 

5 

335 

.52  504  .52  517  .52  530  .52  543 

.52  556 

.52  569 

.52  582  .52  595  .52  608  .52  621 

7 

336 

634    647    650    673 

686 

699 

711    724    737    750 

8 

337 

763    776    789    802 

815 

827 

840    853    866   879 

9 

338 

892    905    917    930 

943 

956 

969    982    994  53  007 

10 

339 

53  020  53  033  53  046  53  058 

53  071 

53  084 

53  097  53  110  53  122    135 

12 

340 

.53148  .53  161  .53173  .53  186 

.53  199 

.53  212 

.53  224  .53  237  .53  250  .53  263 

12 

341 

275  .  288   301    314 

326 

339 

352    364    377    390 

1 

342 

403    415    428    441 

453 

466 

479    491    504    517 

2 

343 

529    542    555    567 

580 

593 

605    618    631    643 

4 

344 

656   668    681    694 

706 

719 

732    744   757    769 

5 

345 

.53  782  .53  794  .53  807  .53  820 

.53  832 

.53  845 

.53  857  .53  870  .53  882  .53  895 

6 

346 

908    920    933    945 

958 

970 

983    995  54  008  54  020 

7 

347 

54  033  54  045  54  058  54  070 

54  083 

54  095 

54  108  54  120    133    145 

8 

348 

158    170    183    195 

208 

220 

233   .  245    258    270 

10 

349 

283    295    307    320 

332 

345 

357    370    382    394 

11 

350 

N 

.54  407  .54  419  .54  432  .54  444 

.54  456 

.54  469 

.54  481  .54  494  .54  506  .54  518 

0     12     3 

4 

5 

6     7    8    9 

,47712  — .54  518 


3500-4000 


N 
350 

0 

1 
.54  419 

2 

3 

4 

5    6 

7 

8 

9 

Dif. 
13 

.54  407 

.54  432 

.54  444 

.54  456 

.54  469  .54  481 

.54  494 

.54  506 

.54  518 

351 

531 

543 

555 

568 

580 

593    605 

617 

630 

642 

1 

352 

654 

667 

679 

691 

704 

716    728 

741 

753 

765 

3 

353 

777 

790 

802 

814 

827 

839    851 

864 

876 

888 

4 

354 

900 

913 

925 

937 

949 

962    974 

986 

998 

55  011 

5 

355 

.55  023 

.55  035 

.55  047 

.55  060 

.55  072 

.55  084  .55  096 

.55  108 

.55  121 

.55  133 

7 

356 

145 

157 

169 

182 

194 

206    218 

230 

242 

255 

8 

357 

267 

279 

291 

303 

315 

328    340 

352 

364 

376 

9 

358 

388 

400 

413 

425 

437 

449    461 

473 

485 

497 

10 

359 

509 

522 

534 

546 

558 

570    582 

594 

606 

618 

12 

360 

.55  630 

.55  642 

.55  654 

.55  666 

.55  678 

.55  691  .55  703 

.55  715 

.55  727 

.55  739 

12 

361 

751 

763 

775 

787 

799 

811    823 

835 

847 

859 

1 

362 

871 

883 

895 

907 

919 

931    943 

955 

967 

979 

2 

363 

991 

66  003 

56  015 

56  027 

56  038 

56  050  56  062 

56  074 

56  086 

56  098 

4 

36+ 

56110 

122 

134 

146 

158 

170    182 

194 

205 

217 

5 

365 

.56  229 

.56  241 

.56  253 

.56  265 

.56  277 

.56  289  .56  301 

.56  312 

.56  324 

.56  336 

6 

366 

348 

360 

372 

384 

396 

407    419 

431 

443 

455 

7 

367 

467 

478 

490 

502 

514 

526    538 

549 

561 

573 

8 

368 

585 

597 

608 

620 

632 

644    656 

667 

679 

691 

10 

369 

703 

714 

726 

738 

750 

761    773 

785 

797 

808 

11 

370 

.56  820 

.56  832 

.56  844 

.56  855 

.56  867 

.56  879  .56  891 

.56  902 

.56  914 

.56  926 

12 

371 

937 

949 

961 

972 

984 

996  57  008 

57  019 

57  031 

57  043 

1 

372 

57  054 

57  066 

57  078 

57  089 

57101 

57  113    124 

136 

148 

159 

2 

373 

171 

183 

194 

206 

217 

229    241 

252 

264 

276 

4 

374 

287 

299 

310 

322 

334 

345    357 

368 

380 

392 

5 

375 

.57  403 

.57  415 

.57  426 

.57  438 

.57  449 

.57  461  .57  473 

.57  484 

.57  496 

.57  507 

6 

376 

519 

530 

542 

553 

565 

576    588 

600 

611 

623 

7 

377 

634 

646 

657 

669 

680 

692    703 

715 

726 

738 

8 

378 

749 

761 

772 

784 

795 

807    818 

830 

841 

852 

10 

379 

864 

875 

887 

898 

910 

921    933 

944 

955 

967 

11 

380 

.57  978 

.57  990 

.58  001 

.58  013 

.58  024 

.58  035  .58  047 

.58  058 

.58  070 

.58  081 

11 

381 

58  092 

58104 

115 

127 

138 

149    161 

172 

184 

195 

1 

382 

206 

218 

229 

240 

252 

263    274 

286 

297 

309 

2 

383 

320 

331 

343 

354 

365 

377   388 

399 

410 

422 

3 

384 

433 

444 

456 

467 

478 

490    501 

512 

524 

535 

4 

385 

.58  546 

.58  557 

.58  569 

.58580 

.58  591 

.58  602  .58  614 

.58  625 

.58  636 

.58  647 

6 

386 

659 

670 

681 

692 

704 

715    726 

737 

749 

760 

7 

387 

771 

782 

794 

805 

816 

827    838 

850 

861 

872 

8 

388 

883 

894 

906 

917 

928 

939    950 

961 

973 

984 

9 

389 

995 

59  006 

59  017 

59  028 

59  040 

59  051  59  062 

59  073 

59  084 

59  095 

10 

390 

.59  106 

.59118 

.59  129 

.59  140 

.59  151 

.59162  .59173 

.59  184 

.59  195 

.59  207 

11 

391 

218 

229 

240 

251 

262 

273'   284 

295 

306 

318 

1 

392 

329 

340 

351 

362 

373 

384    395 

406 

417 

428 

2 

393 

439 

450 

461 

472 

483 

494    506 

517 

528 

539 

3 

394 

550 

561 

572 

583 

594 

605    616 

627 

638 

649 

4 

395 

.59  660 

.59  671 

.59  682 

.59  693 

.59  704 

.59  715  .59  726 

.59  737 

.59  748 

.59  759 

6 

396 

770 

780 

791 

802 

813 

824    835 

846 

857 

868 

7 

397 

879 

890 

901 

912 

923 

934    945 

956 

966 

977 

8 

398 

988 

999 

60  010 

60  021 

60  032 

60  043  60  054 

60065 

60  076 

60  086 

9 

399 

60  097 

60  108 

119 

130 

141 

152    163 

173 

184 

195 

10 

400 

N 

.60  206 

.60  217 

.60  228 

.60  239 

.60  249 

.60  260  .60  271 

.60  282 

.60  293 

.60  304 

0 

1 

2 

3 

4 

5     6 

7 

8 

9 

.54 407 -.60  304 


4000-4500 


N 

0     12     3     4 

5    6     7    8    9 

Dif. 

11 

1 
2 
3 
4 

400 

401 
402 
403 
404 

.60  206  .60  217  .60  228  .60  239  .60  249 
314    325    336   347    358 
423    433    444    455    466 
531    541    552    563    574 
638    649    660    670    681 

.60  260  .60  271  .60  282  .60  293  .60  304 
369    379    390    401    412 

477    487    498    509    520 
584    595    606    617    627 
692    703    713    724    735 

405 
406 
407 
408 
409 

.60  746  .60  756  .60  767  .60  778  .60  788 
853    863    874    885    895 
959    970    981    991  61002 

61066  61077  61087  61098    109 
172    183    194    204    215 

.60  799  .60  810  .60  821  .60  831  .60  842 
906    917    927    938   949 

61013  61023  61034  61045  61055 
119    130    140    151    162 

225    236    247    257    268 

6 

7 

8 

9 

10 

410 

411 
412 
413 
414 

.61  278  .61  289  .61  300  .61  310  .61  321 
384    395    405    416    426 
490    500    511    521    532 
595    606    616    627    637 
700   711    721    731    742 

.61  331  .61  342  .61  352  .61  363  .61  374 
437    448    458   469    479 
542    553        563    574    584 
648    658    669    679    690 

752    763    773    784    794 

11 

1 
2 
3 
4 

415 
416 
417 
418 
419 

.61  805  .61  815  .61  826  .61  836  .61  847 
909    920    930    941    951 

62  014  62  024  62  034  62  045  62  055 
118    128    138    149    159 
221    232    242    252    263 

.61857  .61868  .61878  .61888  .61899 
962    972    982    993  62  003 

62  066  62  076  62  086  62  097    107 
170    180    190    201    211 
273    284    294    304    315 

6 

7 

8 

9 

10 

420 

421 
422 
423 
424 

.62  325  .62  335  .62  346  .62  356  .62  366 
428    439    449    459    469 
531    542    552    562    572 
634    644    655    665    675 
737    747    757    767    778 

.62  377  .62  387  .62  397  .62  408  .62  418 
480    490    500    511    521 
583    593    603    613    624 
685    696    706    716    726 
788    798    808    818    829 

10 

1 
2 
3 
4 

425 
426 
427 
428 
429 

.62  839  .62  849  .62  859  .62  870  .62  880 
941    951    961    972    982 

63  043  63  053  63  063  63  073  63  083 
144    155    165    175    185 
246    256    266    276    286 

.62  890  .62  900  .62  910  .62  921  .62  931 
992  63  002  63  012  63  022  63  033 

63  094    104    114    124    134 
195    205    215    225    236 
296    306    317    327    337 

5 
6 
7 
8 
9 

430 

431 
432 
433 
434 

.63  347  .63  357  .63  367  .63  377  .63  387 
448    458   468    478    488 
548    558    568    579    589 
649    659    669    679    689 
749    759    769    779    789 

.63  397  .63  407  .63  417  .63  428  .63  438 
498    508    518    528    538 
599    609    619    629    639 
699    709    719    729    739 
799    809    819    829    839 

10 

1 
2 
3 
4 

435 
436 
437 
438 
439 

.63  849  .63  859  .63  869  .63  879  .63  889 
949    959    969    979    988 

64  048  64  058  64  058  64  078  64  088 
147    157    167    177    187 
246    256    266    276    286 

.63  899  .63  909  .63  919  .63  929  .63  939 
998  64  008  64  018  64  028  64  038 

64  098    108    118    128    137 
197    207    217    227    237 
296    306    316   326   335 

5 
6 
7 
8 
9 

440 

441 
442 
443 
444 

.64  345  .64  355  .64  365  .64  375  .64  385 
444    454    464    473    483 
542    552    562    572    582 
640   650    660    670    680 

738    748    758    768    777 

.64  395  .64  404  .64  414  .64  424  .64  434 
493    503    513    523    532 
591    601    611    621    631 
689    699    709    719    729 

787    797    807   816   826 

9 

1 

2 
3 

4 

445 
446 
447 
448 
449 

.64  836  .64  846  .64  856  .64  865  .64  875 
933    943    953    963    972 

65  031  65  040  65  050  65  060  65  070 
128    137    147    157    167 
225    234    244    254    263 

.64  885  .64  895  .64  904  .64  914  .64  924 
982    992  65  002  65  011  65  021 

65  079  65  089    099    108    118 
176    186    196    205    215 
273    283    292    302    312 

5 
5 
6 
7 
8 

450 

N 

.65  321  .65  331  .65  341  .65  350  .65  360 

.65  369  .65  379  .65  389  .65  398  .65  408 

_ 

0     12    3    4 

5    6    7    8    9 

.60  206 -.65  408 


4500-5000 


N 

0     12     3     4 

5    6     7    8    9 

Dif. 

10 

1 
2 
3 
4 

450 

451 
452 
453 
454 

.65  321  .65  331  .65  341  .65  350  .65  360 
418   427    437    447    456 
514    523    533    543    552 
610    619    629    639    648 
706   715    725    734   744 

.65  369  .65  379  .65  389  .65  398  .65  408 
466   475    485    495    504 
562    571    581    591    600 
658   667    677    686    696 
753    763    772    782    792 

455 
456 
457 
458 
459 

.65  801  .65  811  .65  820  .65  830  .65  839 
896    906   916   925    935 
992  66  001  66  011  66  020  66  030 

66  087    096    106    115    124 
181    191    200    210    219 

.65  849  .65  858  .65  868  .65  877  .65  887 
944   954    963    973    982 

66  039  66  049  66  058  66  068  66  077 
134    143    153    162    172 
229    238    247    257    266 

5 
6 
7 
8 
9 

460 

461 
462 
463 
464 

.66  276  .66  285  .66  295  .66  304  .66  314 
370    380    389    398    408 
464'   474    483    492    502 
558    567    577    586    596 
652    661    671    680    689 

.66  323  .66  332  .66  342  .66  351  .66  361 
417    427    436   445    455 
511    521    530    539    549 
605    614    624    633    642 
699    708    717    727    736 

9 

1 

2 
3 
4 

465 
466 
467 
468 
469 

.66  745  .66  755  .66  764  .66  773  .66  783 
839    848    857    867    876 
932    941    950   960    969 

67  025  67  034  67  043  67  052  67  062 
117    127    136        145  .  154 

.66  792  .66  801  .66  811  .66  820  .66  829 
885    894    904    913    922 
978    987    997  67  006  67  015 

67  071  67  080  67  089    099    108 
164    173    182    191    201 

I 

6 

7 
8 

470 

471 
472 
473 
474 

.67  210  .67  219  .67  228  .67  237  .67  247 
302    311    321    330    339 
394    403    413    422    431 
486   495    504    514    523 
578   587   596   605    614 

.67  256  .67  265  .67  274  .67  284  .67  293 
348    357    367    376   385 
440   449    459   468    477 
532    541    550    560    569 
624    633    642    651    660 

9 

1 
2 
3 
4 

475 
476 

477 
478 
479 

.67  669  .67  679  .67  688  .67  697  .67  706 
761    770    779   788   797 
852    861    870    879    888 
943    952    961    970   979 

68  034  68  043  68  052  68  061  68  070 

.67  715  .67  724  .67  733  .67  742  .67  752 
806    815    825    834    843 
897    906    916   925    934 
988    997  68  006  68  015  68  024 

68  079  68  088   097    106   115 

5 
5 
6 

7 
8 

480 

481 
482 
483 
484 

.68  124  .68  133  .68  142  .68  151  .68  160 
215    224    233    242    251 
305    314    323    332    341 
395    404    413    422    431 
485    494    502    511    520 

.68  169  .68  178  .68  187  .68  196  .68  205 
260    269    278    287    296 
350    359    368    377    386 
440    449    458    467    476 
529    538    547    556    565 

9 

1 

2 
3 
4 

485 
486 
487 
488 
489 

.68  574  .68  583  .68  592  .68  601  .68  610 
664    673    681    690    699 
753    762    771    780    789 
842    851    860    869    878 
931    940    949    958    966 

.68  619  .68  628  .68  637  .68  646  .68  655 
708    717    726    735    744 
797    806    815    824    833 
886    895    904    913    922 
975    984    993  69  002  69  011 

5 
5 
6 
7 
8 

490 

491 
492 
493 
494 

.69  020  .69  028  .69  037  .69  046  .69  055 
108    117    126    135    144 
197    205    214    223    232 
285    294    302    311    320 
373    381    390    399    408 

.69  064  .69  073  .69  082  .69  090  .69  099 
152    161    170    179    188 
241    249    258    267    276 
329    338    346    355    364 
417  .  425    434    443    452 

8 

1 
2 
2 
3 

495 
496 
497 
498 
499 

.69  461  .69  469  .69  478  .69  487  .69  496 
548    557    566    574    583 
636   644    653    662    671 
723    732    740    749    758 
810    819    827  .   836    845 

.69  504  .69  513  .69  522  .69  531  .69  539 
592    601    609    618    627 
679    688    697    705    714 
767    775    784    793    801 
854    862    871    880    888 

4 
5 
6 
6 
7 

500 

N 

.69  897  .69  906  .69  914  .69  923  .69  932 

.69  940  .69  949  .69  958  .69  966  .69  975 

0     1    2    3    4 

5     6     7     8     9 

.65  321 -.69  975 


10 


5000-5500 


N 

500 

501 
502 
503 
504 

0     12     3     4 

5    6     7    8    9 

Dif. 

9 

1 
2 
3 

4 

.69  897  .69  906  .69  914  .69  923  .69  932 
984    992  70  001  70  010  70  018 

70  070  70  079    088    096    105 
157    165    174    183    191 
243    252    260    269    278 

.69  940  .69  949  .69  958  .69  966  .69  975 

70  027  70  036  70  044  70  053  70  062 

114    122    131    140    148 

200    209    217    226    234 

286    295    303    312    321 

505 
506 
507 
508 
509 

.70  329  .70  338  .70  346  .70  355  .70  364 
415    424    432    441    449 
501    509    518    526    535 
586   595    603   612   621 
672   680   689   697    706 

.70  372  .70  381  .70  389  .70  398  .70  406 
458    467    475    484    492 
544    552    561    569    578 
629    638    646    655    663 
714    723    731    740    749 

5 
5 
6 
7 
8 

510 

511 
512 
513 
514 

.70  757  .70  766  .70.774  .70  783  .70  791 
842    851    859    868    876 
927    935    944    952  -  961 

71012  71020  71029  71037  71046 
096    105    113    122    130 

.70  800  .70  808  .70  817  .70  825  .70  834 
885    893    902    910    919 
969    978    986    995  71003 

71054  71063  71071  71079    088 
139    147    155    164    172 

8 

1 
2 
2 
3 

515 
516 
517 
518 
519 

.71  181  .71  189  .71  198  .71  206  .71  214 
265    273    282    290    299 
349   357.   366   374   383 
433    441    450   458   466 
517    525    533    542    550 

.71  223  .71  231  .71  240  .71  248  .71  257 
307    315    324    332    341 
391   >399    408    416   425 
475    483    492    500    508 
559    567    575    584    592 

4 
5 
6 
6 

7 

520 

521 
522 

523 
524 

.71  600  .71  609  .71  617  .71  625  .71  634 
684    692    700    709    717 
767    775    784    792    800 
850   858   867   875    883 
933   941    950   958   966 

.71  642  .71  650  .71  659  .71  667  .71  675 
725    734    742    750    759 
809    817    825    834    842 
892    900    908    917    925 
975    983    991    999  72  008 

8 

1 
2 
2 
3 

525 
526 
527 
528 
529 

.72  016  .72  024  .72  032  .72  041  .72  049 
099    107    115    123    132 
181    189    198    206    214 
263    272    280    288    296 
346   354   362   370   378 

.72  057  .72  066  .72  074  .72  082  .72  090 
140    148    156    165    173 
222    230    239    247    255 
304    313    321    329    337 
387    395    403    411    419 

4 
5 
6 
6 

7 

530 

531 
532 
533 
534 

.72  428  .72  436  .72  444  .72  452  .72  460 
509    518    526    534   "542 
591    599    607    616    624 
673   681    689   697    705 
754   762    770   779    787 

.72  469  .72  477  .72  485  .72  493  .72  501 
550    558    567    575    583 
632    640    648    656    665 
713    722    730    738    746 
795    803    811    819   827 

8 

1 
2 
2 
3 

535 
536 
537 
538 
539 

.72  835  .72  843  .72  852  .72  860  .72  868 
916    925    933    941    949 
997  73  006  73  014  73  022  73  030 

73  078   086   094   102  .  Ill 
159   167    175    183    191 

.72  876  .72  884  .72  892  .72  900  .72  908 
957   965    973   981   989 

73  038  73  046  73  054  73  062  73  070 
119   127    135    143    151 
199    207    215    223    231 

4 
5 
6 
6 
7 

540 

541 

542 
543 
544 

.73  239  .73  247  .73  255  .73  263  .73  272 
320    328    336    344    352 
400    408   416   424    432 
480   488    496    504    512 
560    568    576    584    592 

.73  280  .73  288  .73  296  .73  304  .73  312 
360    368    376    384    392 
440    448    456   464    472 
520    528    536    544    552 
600    608    616   624    632 

7 

1 
1 
2 
3 

545 
546 
547 
548 
549 

.73  640  .73  648  .73  656  .73  664  .73  672 
719    727    735    743    751 
799    807    815    823    830 
878    886    894    902    910 
957    965    973    981    989 

.73  679  .73  687  .73  695  .73  703  .73  711 
759    767    775    783    791 
838    846    854    862    870 
918    926   933    941    949 
997  74  005  74  013  74  020  74  028 

4 
4 
5 
6 
6 

550 

N 

.74  036  .74  044  .74  052  .74  060  .74  068 

.74  076  .74  084  .74  092  .74  099  .74  107 

--- 

0     12     3    4 

5    6     7    8    9 

.69  897 -.74 107 


5500-6000  11 


N 

0     12    3    4 

5    6     7    8    9 

Dif. 

650 

551 

552 
553 
554 

.74  036  .74  044  .74  052  .74  060  .74  068 
115    123    131    139    147 
194    202    210    218    225 
273    280    288    296   304 
351    359   367   374   382 

.74  076  .74  084  .74  092  .74  099'  .74  107 
155    162    170    178    186 
233    241    249    257    265 
312    320    327    335    343 
390    398   406    414    421 

8 

1 
2 
2 
3 

555 
556 
557 
55S 
559 
< 
660 
561 
562 
563 
564 

.74  429  .74  437  .74  445  .74  453  .74  461 
507    515    523    531    539 
586    593    601    609    617 
663    671    679    687    695 
741    749    757    764    772 

.74  468  .74  476  .74  484  .74  492  .74  500 
547    554    562    570    578 
624    632    640    648    656 
702    710    718    726    733 
780   788   796   803    811 

4 

5 
6 
6 

7 

.74  819  .74  827  .74  834  .74  842  .74  850 
896    904    912    920    927 
974    981    989    997  75  005 

75  051  75  059  75  066  75  074    082 
128    136    143    151    159 

.74  858  .74  865  .74  873  .74  881  .74  889 
935    943    950    958    966 

75  012  75  020  75  028  75  035  75  043 
089    097    105    113    120 
166   174    182    189   197 

7 
1 
1 
2 
3 

565 
566 
567 
568 
569 

.75  205  .75  213  .75  220  .75  228  .75  236 
282    289    297    305    312 
358    366    374    381    389 
435    442    450    458    465 
511    519    526    534    542 

.75  243  .75  251  .75  259  .75  266  .75  274 
320    328    335    343    351 
397    404    412    420   427 
473    481    488    496    504 
549   557    565    572   580 

4 
4 
5 
6 
6 

570 

571 

572 
573 
574 

.75  587  .75  595  .75  603  .75  610  .75  618 
664    671    679    686   694 
740    747    755    762    770 
815    823    831    838    846 
891    899    906    914    921 

.75  626  .75  633  .75  641  .75  648  .75  656 
702    709   717    724    732 
778    785    793    800   808 
853    861    868    876    884 
929    937    944    952    959 

8 

1 
2 
2 
3 

575 
576 
577 
578 
579 

.75  967  .75  974  .75  982  .75  989  .75  997 

76  042  76  050  76  057  76  065  76  072 

118.   125    133    140    148 

193    200   -208    215    223 

268    275    283    290    298 

.76  005  .76  012  .76  020  .76  027  .76  035 
080    087    095    103    110 
155    163    170    178    185 
230    238    245    253    260 
305    313   320   328   335 

4 

5 
6 
6 

7 

680 

581 

582 
583 
584 

.76  343  .76  350  .76  358  .76  365  .76  373 
418    425    433    +40   448 
492    500    507    515    522 
567    574    582    589    597 
641    649  jbl^        664    671 

.76  380  .76  388  .76  395  .76  403  .76  410 
455    462    470   477    485 
530    537    545    552    559 
604    612    619    626    634 
678   686   693    701    708 

7 
1 
1 
2 
3 

585 
586 
587 
588 
589 

.76  716  .76  723  .76  730  .76  738  .76  745 
790    797    805    812    819 
864    871    879    886    893 
938    945    953    960    967 

77  012  77  019  77  026  77  034  77  041 

.76  753  .76  760  .76  768  .76  775  .76  782 
827    834    842    849    856 
901    908    916    923    930 
975    982    989    997  77  004 

77  048  77  056  77  063  77  070   073 

4 
4 
5 
6 
6 

590 

591 

592 
593 
594 

.77  085  .77  093  .77100  .77  107  .77115 
159    166    173    181    188 
232    240    247    254    262 
305    313    320    327    335 
379    386   393    401    408 

.77  122  .77  129  .77  137  .77  144  .77  151 
195    203    210    217    225 
269    276    283    291    298 
342    349    357    364    371 
415    422    430    437   444 

7 

1 
1 
2 
3 

595 
596 
597 
598 
599 

.77  452  .77  459  .77  466  .77  474  .77  481 
525    532    539    546    554 
597    605    612    619    627 
670    677    685    692    699 
743    750    757    764    772 

.77  488  .77  495  .77  503  .77  510  .77  517 
561    568    576    583    590 
634    641    648    656    663 
706    714    721    728    735 
779    786*0  793  d   801    808 

4 
4 
5 
6 
6 

600 

.77  815  .77  822  .77  830  .77  837  .77  844 

.77  851  .77  859  .77  866  .77  873  .77  880 

N 

0     12    3    4 

5     6     7    8    9 

74  036 -,77  880 


12 


6000-6500 


N 
600 

0 

1     2     3 

4 

5    6    7    8    9 

Dif. 
8 

.77  815 

.77  822  .77  830  .77  837 

.77  844 

.77  851  .77  859  .77  866  .77  873  .77  880 

601 

887 

895    902    909 

916 

924    931    938    945    952 

1 

602 

960 

967    974    981 

988 

996  78  003  78  010  78  017  78  025 

2 

603 

78  032 

78  039  78  046  78  053 

78  061 

78  068    075    082    089    097 

2 

604 

104 

111    118    125 

132 

140    147    154    161    168 

3 

60S 

.78  176 

.78  183  .78  190  .78  197 

.78  204 

.78  211  .78  219  .78  226  .78  233  .78  240 

4 

606 

247 

254    262    269 

276 

283    290    297    305    312 

5 

607 

319 

326    333    340 

347 

355    362    369   376   38'3 

6 

608 

390 

398    405    412 

419 

426    433    440   447    455 

6 

609 

462 

469   476    483 

490 

497    504    512    519    526 

^  7 

610 

.78  533 

.78  540  .78  547  .78  554 

.78  561 

.78  569  .78  576  .78  583  .78  590  .78  597 

7 

611 

604 

611    618    625 

633 

640    647    654    661    668 

1 

612 

675 

682    689    696 

704 

711    718   725    732   739 

1 

613 

746 

753    760    767 

774 

781    789   796   803   810 

2 

614 

817 

824    831    838 

845 

852    859   866   873   880 

3 

615 

.78  888 

.78  895  .78  902  .78  909 

.78  916 

.78  923  .78  930  .78  937  .78  944  .78  951 

4 

616 

958 

965    972    979 

986 

993  79  000  79  007  79  014  79  021 

4 

617 

79  029 

79  036  79  043  79  050 

79  057 

79  064    071    078   085    092 

5 

618 

099 

106    113    120 

127 

134    141    148    155    162 

6 

619 

169 

176    183    190 

197 

204    211    218   225    232 

6 

620 

.79  239 

.79  246  .79  253  .79  260 

.79  267 

.79  274  .79  281  .79  288  .79  295  .79  302 

7 

621 

309 

316   323    330 

337 

344    351    358   365    372 

1 

622 

379 

386   393    400 

407 

414    421    428    435    442 

1 

623 

449 

456   463    470 

477 

484    491    498    505    511 

2 

624 

518 

525    532    539 

546 

553   560   567   574   581 

3 

625 

.79  588 

.79  595  .79  602  .79  609 

.79  616 

.79  623  .79  630  .79  637  .79  644  .79  650 

4 

626 

657 

664    671    678 

685 

692    699    706    713    720 

4 

627 

727 

734    741    748 

754 

761    768   775    782    789 

5 

628 

796 

803    810    817 

824 

831    837    844    851    858 

6 

629 

865 

872    879    886 

893 

900    906    913    920   927 

6 

630 

.79  934 

.79  941  .79  948  .79  955 

.79  962 

.79  969  .79  975  .79  982  .79  989  .79  996 

7 

631 

80  003 

80  010  80  017  80  024 

80  030 

80  037  80  044  80  051  80  058  80  065 

1 

632 

072 

079   085    092 

099 

106    113    120    127    134 

1 

633 

140 

147    154    161 

168 

175    182    188    195    202 

2 

634 

209 

216    223    229 

236 

243    250    257    264    271 

3 

635 

.80  277 

.80  284  .80  291  .80  298 

.80  305 

.80  312  .80318  .80  325  .80  332  .80  339 

4 

636 

346 

353    359    366 

373 

380    387    393    400   407 

4 

637 

414 

421    428    434 

441 

448    455    462    468   475 

5 

638 

482 

489   496    502 

509 

516    523    530    536    543 

6 

639 

550 

557    564    570 

577 

584    591    598    604    611 

6 

640 

.80  618 

.80  625  .80  632  .80  638 

.80  645 

.80  652  .80  659  .80  665  .80  672^.80  679 

6 

641 

686 

693    699    706 

713 

720    726    733    740    747 

1 

642 

754 

760    767    774 

781 

787    794    801    808   814 

1 

643 

821 

828    835    841 

848 

855    862    868    875    882 

2 

644 

889 

895    902    909 

916 

922    929    936   943    949 

2 

645 

.80  956 

.80  963  .80  969  .80  976 

.80  983 

.80  990  .80  996  .81003  .81010  .81017 

3 

646 

81023 

81030  81037  81043 

81  050 

81057  81064    070   077    084 

4 

647 

090 

097    104    111 

117 

124    131    137    144    151 

4 

648 

158 

164    171    178 

184 

191    198    204    211    218 

5 

649 

224 

231    238    245 

251 

258    265    271    278    285 

5 

650 

N 

.81  291 

.81298  .81305  .81311 

.81318 

.81  325  .81  331  .81  338  .81  345  .81  351 

0 

1     2     3 

4 

5     6     7    8    9 

.77  815  — .81351 


6500-7000 


13 


650 

651 
652 
653 
654 

655 
656 
657 
658 
659 


661 
662 
663 
664 

665 
666 
667 
668 
669 

670 

671 
672 
673 
674 

675 
676 
677 
678 
679 


681 
682 
683 
684 

685 
686 
687 
688 
689 

690 

691 
692 
693 
694 

695 
696 
697 
698 
699 

700 


N 


.81  291  .81  298  .81  305  .81  311  .81  318 

358    365    371  378    385 

425    431    438  445    451 

491    498    505  511    518 

558    564    571  578    584 

.81  624  .81  631  .81  637  .81  644  .81  651 

690    697    704  710    717 

757   763    770  776   783 

823    829    836  842    849 

889    895    902  908    915 

.81  954  .81  961  .81  968  .81  974  .81  981 

82  020  82  027  82  033  82  040  82  046 
086  092  099  105  112 
151  158  164  171  178 
217    223    230  236    243 

.82  282  .82  289  .82  295  .82  302  ,82  308 

347    354    360  367    373 

413    419    426  432    439 

478    484   491  497    504 

543    549    556  562    569 

.82  607  .82  614  .82  620  .82  627  .82  633 

672    679    685  692    698 

737    743    750  756    763 

802    808    814  821    827 

866    872    879  885    892 

.82  930  .82  937  .82  943  .82  950  .82  956 

995  83  001  83  008  83  014  83  020 

83  059  065  072  078  085 
123  129  136  142  149 
187    193    200  206    213 

.83  251  .83  257  .83  264  .83  270  .83  276 

315    321    327  334    340 

378    385    391  398   404 

442    448    455  461    467 

506    512    518  525    531 

.83  569  .83  575  .83  582  .83  588  .83  594 

632    639    645  651    658 

696    702    708  715    721 

.759    765    771  778    784 

^,822    828    835  841    847 

.83  885  .83  891  .83  897  .83  904  .83  910 

948   954    960  967    973 

84  011  84  017  8-1023  84  029  84  036 
073  080  086  092  098 
136    142    148  155    161 

.84198  .84  205  .84  211  .84  217  .84  223 

261    267    273  280    286 

323    330   336  342    348 

386    392    398  404    410 

448   454   460  466    473 


.81  325  .81  331  .81  338  .81  345  .81  351 

391    398  405  411    418 

458    465  471  478   485 

525    531  538  544    551 

591    598  604  611    617 

.81  657  .81  664  .81  671  .81  677  .81  684 

723    730  737  743    750 

790    796  803  809    816 

856    862  869  875    882 

921    928  935  941    948 

.81  987  .81  994  .82  000  .82  007  .82  014 

82  053  82  060  066  073  079 
119  125  132  138  145 
184  191  197  204  210 
249    256  263  269    276 

.82  315  .82  321  .82  328  .82  334  .82  341 

380    387  393  400   406 

445    452  458  465    471 

510    517  523  530   536 

575    582  588  595    601 

.82  640  .82  646  .82  653  .82  659  .82  666 

705    711  718  724    730 

769    776  782  789    795 

834    840  847  853    860 

898   905  911  918   924 

.82  963  .82  969  .82  975  .82  982  .82  988 

83  027  83  033  83  040  83  046  83  052 
091  097  104  110  117 
155  161  168  174  181 
219    225  232  238    245 

.83  283  .83  289  .83  296  .83  302  .83  308 

347    353  359  366    372 

410    417  423  429    436 

474    480  487  493    499 

537    544  550  556    563 

.83  601  .83  607  .83  613  .83  620  .83  626 

664    670  677  683    689 

727    734  740  746    753 

790    797  803  809    816 

853    860  866  872    879 

.83  916  .83  923  .83  929  .83  935  .83  942 

979    985  992  998  84  004 

84  042  84  048  84  055  84  061  067 
105  111  117  123  130 
167    173  180  186    192 

.84  230  .84  236  .84  242  .84  248  .84  255 

292    298  305  311    317 

354    361  367  373    379 

417    423  429  435    442 

479   485  491  497    504 


.84  510  .84  516 -.84  522  .84  528  .84  535  .84  541  .84  547  .84  553  .84  559  .84  566 


Dif. 

6 

1 
1 

2 
2 

3 
4 
4 

5 
5 

7 
1 
1 

2 
3 

4 
4 
5 
6 
6 

6 

1 

1 
2 
2 

3 
4 
4 

5 
5 

7 
1 
1 

2 
3 

4 

4 
5 
6 
6 

6 

1 
1 
2 

2 

3 

4 
4 

5 
5 


.81291  — .84  566 


14 


7000-7500 


700 

701 
702 
703 
704 

705 
706 
707 
708 
709 

710 

711 
712 
713 
714 

715 
716 
7]7 
718 
719 

720 

721 
722 
723 
724 

725 
726 
727 
728 
729 

730 

731 
732 
733 
734 

735 
736 
737 
738 
739 

740 

741 
742 
743 
744 

745 
746 
747 
748 
749 

750 


.84  510  .84  516  .84  522  .84  528  .84  535 

572    578    584    590  597 

634    640    646    652  658 

696    702    708    714  720 

757   763    770   776  782 

.84  819  .84  825  .84  831  .84  837  .84  844 

880    887    893    899  905 

942    948   954    960  967 

85  003  85  009  85  016  85  022  85  028 

065    071   077   083  089 

.85  126  .85  132  .85  138  .85  144  .85  150 

187    193    199   205  211 

248    254    260    266  272 

309   315    321    327  333 

370   376   382   388  394 

.85  431  .85  437  .85  443  .85  449  .85  455 

491    497   503   509  516 

552   558   564   570  576 

612    618    625    631  637 

673   679   685    691  697 

.85  733  .85  739  .85  745  .85  751  .85  757 

794    800    806    812  818 

854    860    866    872  878 

914    920    926    932  938 

974    980    986    992  998 

.86  034  .86  040  .86  046  .86  052  .86  058 

094    100    106    112  118 

153    159    165    171  177 

213    219    225    231  237 

273  279    285    291  297 

.86  332  .86  338  .86  344  .86  350  .86  356 

392    398    404    410  415 

451    457   463   469  475 

510    516    522    528  534 

570   576   581    587  593 

.86  629  .86  635  .86  641  .86  646  .86  652 

688   694    700   705  711 

747    753    759   764  770 

806    812    817    823  829 

864   870   876   882  888 

.86  923  .86  929  .86  935  .86  941  .86  947 

982    988    994    999  87  005 

87  040  87  046  87  052  87  058  064 

099    105    111    116  122 

157    163    169    175  181 

.87  216  .87  221  .87  227  .87  233  .87  239 

274  280  286  291  297 
332  338  344  349  355 
390  396  402*  408  413 
448    454    460   466  471 


.84  541  .84  547  .84  553  .84  559  .84  566 

603    609    615  621  628 

665    671    677  683  689 

726    733    739  745  751 

788    794    800  807  813 

.84  850  .84  856  .84  862  .84  868  .84  874 

911    917    924  930  936 

973    979    985  991  997 

85  034  85  040  85  046  85  052  85  058 
095    101    107  114  120 

.85  156  .85  163  .85  169  .85  175  .85  181 

217    224    230  236  242 

278    285    291  297  303 

339   345    352  358  364 

400   406   412  418  425 

.85  461  .85  467  .85  473  .85  479  .85  485 

522    528    534  540  546 

582    588    594  600  606 

643    649    655  661  667 

703    709    715  721  727 

.85  763  .85  769  .85  775  .85  781  .85  788 

824    830    836  842  848 

884    890    896  902  908 

944    950    956  962  968 

86  004  86  010  86  016  86  022  86  028 

.86  064  .86  070  .86  076  .86  082  .86  088 

124    130    136  141  147 

183    189    195  201  207 

243    249    255  261  267 

303    308    314  320  326 

.86  362  .86  368  .86  374  .86  380  .86  386 

421    427    433  439  445 

481    487    493  499  504 

540    546    552  558  564 

599    605    611  ■  617  623 

.86  658  .86  664  .86  670  .86  676  .86  682 

717    723    729  735  741 

776    782    788  794  800 

835    841    847  853  859 

894    900    906  911  917 

.86  953  .86  958  .86  964  .86  970  .86  976 

87  011  87  017  87  023  87  029  87  035 
070  075  081  087  093 
128  134  140  146  151 
186    192    198  204  210 

.87  245  .87  251  .87  256  .87  262  .87  268 

303    309    315  320  326 

361    367    373  379  384 

419    425    431  437  442 

477    483    489  495  500 


.87  506  .87  512  .87  518  .87  523  .87  529  .87  535  .87  541  .87  547  .87  552  .87  558 


Dif. 


.84  510 -.87  558 


7500-8000 


15 


N 
750 

0 

1 

2 

.87  518 

3 

4 

5 

6     7     8 

9 

Dif. 
6 

.87  506 

.87  512 

.87  523 

.87  529 

.87  535 

.87  541  .87  547  .87  552 

.87  558 

751 

564 

570 

576 

581 

587 

593 

599   604    610 

616 

1 

752 

622 

628 

633 

639 

645 

651 

656    662    668 

674 

1 

753 

679 

685 

691 

697 

703 

708 

714    720    726 

731 

2 

754 

737 

743 

749 

754 

760 

766 

772   777    783 

789 

2 

755 

.87  795 

.87  800 

.87  806 

.87  812 

.87  818 

.87  823 

.87  829  .87  835  .87  841 

.87  846 

3 

756 

852 

858 

864 

869 

875 

881 

887    892    898 

904 

4 

757 

910 

915 

921 

927 

933 

938 

944    950   955 

961 

4 

758 

967 

973 

978 

984 

990 

996 

88  001  88  007  88  013 

88  018 

5 

759 

88  024 

88  030 

88  036 

88  041 

88  047 

88  053 

058    064    070 

076 

5 

760 

.88  081 

.88  087 

.88  093 

.88  098 

.88  104 

.88  110 

.88116  .88121  .88127 

.88  133 

5 

761 

138 

144 

150 

156 

161 

167 

173    178   184 

190 

1 

762 

195 

201 

207 

213 

218 

224 

230    235    241 

247 

1 

763 

252 

258 

264 

270 

275 

281 

287    292    298 

304 

2 

764 

309 

315 

321 

326 

332 

338 

343   349   355 

360 

2 

765 

.88  366 

.88  372 

.88  377 

.88  383 

.88  389 

.88  395 

.88  400  .88  406  .88  412 

.88  417 

3 

766 

423 

429 

434 

440 

446 

451 

457    463    468 

474 

3 

767 

480 

485 

491 

497 

502 

508 

513    519    525 

530 

4 

768 

536 

542 

547 

553 

559 

564 

570    576    581 

587 

4 

769 

593 

598 

604 

610 

615 

621 

627    632    638 

643 

5 

770 

.88  649 

.88  655 

.88  660 

.88  666 

.88  672 

.88  677 

.88  683  .88  689  .88  694 

.88  700 

6 

771 

705 

711 

717 

722 

728 

734 

739    745    750 

756 

1 

772 

762 

767 

773 

779 

784 

790 

795    801  •   807 

812 

1 

773 

818 

824 

829 

835 

840 

846 

852    857    863 

868 

2 

774 

874 

880 

885 

891 

897 

902 

908    913    919 

925 

2 

775 

.88  930 

.88  936 

.88  941 

.88  947 

.88  953 

.88  958 

.88  964  .88  969  .88  975 

.88  981 

3 

776 

986 

992 

997 

89  003 

89  009 

89  014 

89  020  89  025  89  031 

89  037 

4 

777 

89  042 

89  048 

89  053 

059 

064 

070 

076   081    087 

092 

4 

778 

098 

104 

109 

115 

120 

126 

131    137    143 

148 

5 

779 

154 

159 

165 

170 

176 

182 

187    193    198 

204 

5 

780 

.89  209 

.89  215 

.89  221 

.89  226 

.89  232 

.89  237 

.89  243  .89  248  .89  254 

.89  260 

5 

781 

265 

271 

276 

282 

287 

293 

298   304    310 

315 

1 

782 

321 

326 

332 

337 

343 

348 

354    360    365 

371 

1 

783 

376 

382 

387 

393 

398 

404 

409    415    421 

426 

2 

784 

432 

437 

443 

448 

454 

459 

465    470    476 

481 

2 

785 

.89  487 

.89  492 

.89  498 

.89  504 

.89  509 

.89  515 

.89  520  .89  526  .89  531 

.89  537 

3 

786 

542 

548 

553 

559 

564 

570 

575    581    586 

592 

3 

787 

597 

603 

609 

614 

620 

625 

631    636    642 

647 

4 

788 

653 

658 

664 

669 

675 

680 

686    691    697 

702 

4 

789 

708 

713 

719 

724 

730 

735 

741    746   752 

757 

5 

790 

.89  763 

.89  768 

.89  774 

.89  779 

.89  785 

.89  790 

.89  796  .89  801  .89  807 

.89  812 

6 

791 

818 

823 

829 

834 

840 

845 

851    856    862 

867 

1 

792 

873 

878 

883 

889 

894 

900 

905    911    916 

922 

1 

793 

927 

933 

938 

944 

949 

955 

960    966    971 

977 

2 

794 

982 

988 

993 

998 

90  004 

90  009 

90  015  90  020  90  026 

90  031 

2 

795 

.90  037 

.90  042 

.90  048 

.90  053 

.90  059 

.90  064 

.90  069  .90  075  .90  080 

.90  086 

3 

796 

091 

097 

102 

108 

113 

119 

124    129    135 

140 

4 

797 

146 

151 

157 

162 

168 

173 

179    184    189 

195 

4 

798 

200 

206 

211 

217 

222 

227 

233    238    244 

249 

5 

799 

255 

260 

266 

271 

276 

282 

287    293    298 

304 

5 

800 

N 

.90  309 

.90  314 

.90  320 

.90  325 
3 

.90  331 

.90  336 

.90  342  .90  347  .90  352 

.90  358 

0 

1 

2 

4 

5 

6     7    8 

9 

.87  506 -.90  358 


16 


8000-8500 


N 

800 

SOI 
802 
803 
804 

0     12 

3    4 

5 

6    7    8    9 

Dif. 

5 

1 

1 
2 
2 

.90  309  .90  314  .90  320 
363    369    374 
417   423    428 
472    477    482 
526    531    536 

.90  325  .90  331 
380    385 
434    439 
488    493 
542    547 

.90  336 
390 
445 
499 
553 

.90  342  .90  347  .90  352  .90  358 
396   401    407    412 
450    455    461    466 
504    509    515    520 
558    563    569    574 

805 
806 
807 
808 
809 

.90  580  .90  585  .90  590 
634    639    644 
687    693    698 
741    747    752 
795    800    806 

.90  596  .90  601 
650    655 
703    709 
757    763 
811    816 

.90  607 
660 
714 

768 

822 

.90  612  .90  617  .90  623  .90  628 
666   671    677    682 
720    725    730    736 
773    779    784    789 
827    832    838    843 

3 
3 
4 

4 

5 

810 

811 
812 
813 
814 

.90  849  .90  854  .90  859 
902    907    913 
956   961    966 

91009  91014  91020 
062    068    073 

.90  865  .90  870 
918    924 
972    977 

91025  91030 
078    084 

.90  875 
929 
982 

91036 
089 

.90  881  .90  886  .90  891  .90  897 
934    940    945    950 
988    993    998  91004 

91041  91046  91052    057 
094    100    105    110 

6 

1 

1 
2 
2 

815 
816 
817 
818 
819 

.91  116  .91  121  .91  126 
169    174    180 
222    228    233 
275    281    286 
328    334    339 

.91  132  .91  137 

185    190 
238    243 
291    297 
344    350 

.91  142 
196 
249 
302 
355 

.91  148  .91  153  .91  158  .91  164 
201    206    212    217 
254    259    265    270 
307    312    318    323 
360    365    371    376 

3 

4 

4 

5 
5 

820 

821 
822 
823 
824 

.91  381  .91  387  .91  392 
434    440   445 
487    492    498 
540    545    551 
593    598    603 

.91  397  .91  403 
450   455 
503    508 
556    561 
609    614 

.91  408 
461 
514 
566 
619 

.91  413  .91  418  .91  424  .91  429 
466    471    477    482 
519    524    529    535 

572    577    582    587 
624   630    635    640 

5 

1 
1 
2 

2 

825 
826 
827 
828 
829 

.91645  .91651  .91656 
698   703    709 
751    756   761 

803    808    814 
855    861    866 

.91661  .91666 
714    719 
766    772 
819    824 
871   876 

.91  672 
724 

777 
829 
882 

.91  677  .91  682  .91  687  .91  693 

730    735    740    745 
782    787    793    798 
834    840    845    850 
887   892   897   903 

3 
3 
4 

4 

5 

830 

831 
832 
833 
834 

.91  908  .91  913  .91  918 
960   965    971 

92  012  92  018  92  023 
065    070   075 
117    122    127 

.91  924  .91  929 
976    981 

92  028  92  033 
080   085 
132    137 

.91  934 
986 

92  038 
091 
143 

.91  939  .91  944  .91  950  .91  955 
991    997  92  002  92  007 

92  044  92  049    054    059 
096    101    106    111 
148    153    158    163 

6 

1 
1 
2 
2 

835 
836 

837 
838 
839 

.92  169  .92  174  .92  179 
221    226    231 
273    278    283 
324    330    335 
376   381    387 

.92  184  .92  189 
236    241 
288    293 
340    345 
392    397 

.92  195 
247 
298 
350 
402 

.92  200  .92  205  .92  210  .92  215 
252    257    262    267 
304    309   314    319 
355    361    366    371 
407    412    418   423 

3 
4 
4 

5 
5 

840 

841 
842 
843 
844 

.92  428  .92  433  .92  438 
480   485    490 
531    536   542 
583    588   593 
634   639   645 

.92  443  .92  449 
495    500 
547    552 
598    603 
650   655 

.92  454 
505 
557 
609 
660 

.92  459  .92  464  .92  469  .92  474 
511    516    521    526 
562    567    572    578 
614    619    624    629 
665    670    675    681 

5 

1 
1 

2 
2 

845 
846 
847 
848 
849 

.92  686  .92  691  .92  696 
737    742    747 
788   793    799 
840   «45    850 
891    896    901 

.92  701  .92  706 

752    758 
804    809 
855    860 
906   911 

.92  711 
763 
814 
865 
916 

.92  716  .92  722  .92  727  .92  732 
768    773    778    783 
819    824    829    834 
870    875    881    886 
921    927    932    937 

3 
3 

4 
4 

5 

850 

N 

.92  942  .92  947  .92  952 

.92  957  .92  962 

.92  967 

.92  973  .92  978  .92  983  .92  988 

0     1    2 

3    4 

5 

6     7    8    9 

.90  309 -.92  988 


8500-9000 


17 


830 

851 
852 
853 
854 

855 
856 

857 
858 
859 

830 

861 
862 
863 
86+ 

865 
866 
867 
868 
869 

870 

871 
872 
873 
874 

875 
876 
877 
878 
879 

880 

881 

882 
883 
884 

885 
886 
887 
888 
889 


891 
892 
893 
894 

895 
896 
897 
898 
899 

900 


N 


.92  942  .92  947  .92  952  .92  957  .92  962 

993    998  93  003  93  008  93  013 

93  044  93  049    054    059  064 

095    100    105    110  115 

146    151    156    161  166 

,93  197  .93  202  .93  207  .93  212  .93  217 
247  252  258  263  268 
298  303  308  313  318 
349  354  359  364  369 
399    404    409    414    420 


.93  450 
500 
551 
601 
651 

.93  702 

752 
802 
852 
902 


.93  455 
505 
556 
606 
656 

.93  707 

757 
807 
857 
907 


.93  460 
510 
561 
611 
651 

.93  712 
762 
812 
862 
912 


.93  465 
515 
566 
616 
666 

.93  717 

767 
817 
867 
917 


.93  470 
520 
571 
621 
671 

.93  722 
772 
822 
872 
922 


.93  952  .93  957  .93  962  .93  967  .93  972 

94  002  94  007  94  012  94  017  94  022 
052  057  052  067  072 
101  106  111  116  121 
151    156    161    166  171 

.94  201  .94  206  .94  211  .94  216  .94  221 

250    255    260    265  270 

300   305    310    315  320 

349    354    359    364  369 

399    404    409   414  419 

.94  448  .94  453  .94  458  .94  463  .94  468 

498    503    507    512  517 

547    552    557    562  567 

596    601    606    611  616 

645    650    655    660  665 

.94  694  .94  699  .94  704  .94  709  .94  714 

743    748    753    758  763 

792    797    802    807  812 

841    846    851    856  861 

890    895    900    905  910 

.94  939  .94  944  .94  949  .94  954  .94  959 

988    993    998  95  002  95  007 

95  036  95  041  95  0+6  051  056 
085  090  095  100  105 
134    139    143    148  153 

.95  182  .95  187  .95  192  .95  197  .95  202 

231    236    240    245  250 

279    284    289    294  299 

328    332    337    342  347 

376    381    386    390  395 


.92  967  .92  973  .92  978  .92  983  .92  988 

93  018  93  024  93  029  93  034  93  039 
069  075  080  085  090 
120  125  131  136  141 
171    176  181  186  192 

.93  222  .93  227  .93  232  .93  237  .93  242 

273    278  283  288  293 

323    328  334  339  344 

374    379  384  389  394 

425    430  435  440  445 

.93  475  .93  480  .93  485  .93  490  .93  495 

526    531  536  541  546 

576    581  586  591  596 

626   631  636  641  646 

676   682  687  692  697 

.93  727  .93  732  .93  737  .93  742  .93  747 

777    782  787  792  797 

827    832  837  842  847 

877    882  887  892  897 

927    932  937  942  947 

.93  977  .93  982  .93  987  .93  992  .93  997 

94  027  94  032  94  037  94  042  94  047 
077  082  086  091  096 
126  131  136  141  146 
176    181  186  191  196 

.94  226  .94  231  .94  236  .94  240  .94  245 

275    280  285  290  295 

325    330  335  340  345 

374    379  384  389  394 

424    429  433  438  443 

.94  473  .94  478  .94  483  .94  488  .94  493 

522    527  532  537  542 

571    576  581  586  591 

621    626  630  635  640 

670    675  680  685  689 

.94  719  .94  724  .94  729  .94  734  .94  738 

768    773  778  783  787 

817    822  827  832  836 

866   871  876  880  885 

915    919  924  929  934 

.94  963  .94  968  .94  973  .94  978  .94  983 

95  012  95  017  95  022  95  027  95  032 
061  066  071  075  080 
109  114  119  124  129 
158    163  168  173  177 

.95  207  .95  211  .95  216  .95  221  .95  226 

255    260  265  270  274 

303    308  313  318  323 

352    357  361  366  371 

400    405  410   415  419 


.95  424  .95  429  .95  434  .95  439  .95  444  .95  448  .95  453  .95  458  .95  463  .95  468 


Dif. 

6 

1 

1 
2 
2 

3 

4 
4 

5 
5 

5 

1 

1 
2 

2 

3 
3 

4 
4 

5 

4 

0 
1 
1 

2 

2 
2 
3 
3 
4 

5 

1 
1 

2 
2 

3 
3 
4 

4 

5 

4 

0 
1 
1 
2 

2 
2 
3 
3 
4 


.92  942 -.95  468 


18 


9000-9500 


N 
900 

0 

12     3 

4 

5 

6 

7    8    9 

Dif. 
5 

.95  424 

.95  429  .95  434  .95  439 

.95  444 

.95  448 

.95  453 

.95  458  .95  463  .95  468 

901 

472 

477    482    487 

492 

497 

501 

506    511    516 

1 

902 

521 

525    530    535 

540 

545 

550 

554    559    564 

1 

903 

569 

574    578    583 

588 

593 

598 

602    607    612 

2 

904 

617 

622    626    631 

636 

641 

646 

650    655    660 

2 

905 

.95  665 

.95  670  .95  674  .95  679 

.95  684 

.95  689 

.95  694 

.95  698  .95  703  .95  708 

3 

906 

713 

718    722    727 

732 

737 

742 

746    751    756 

3 

907 

761 

766    770    775 

780 

785 

789 

794    799    804 

4 

908 

809 

813    818    823 

828 

832 

837 

842    847    852 

4 

909 

856 

861    866    871 

875 

880 

885 

890    895    899 

5 

910 

.95  904 

.95  909  .95  914  .95  918 

.95  923 

.95  928 

.95  933 

.95  938  .95  942  .95  947 

4 

911 

952 

957    961    966 

971 

976 

980 

985    990    995 

0 

912 

999 

96  004  96  009  96  014 

96  019 

96  023 

96  028 

96  033  96  038  96  042 

1 

913 

96  047 

052    057    061 

066 

071 

076 

080    085    090 

1 

914 

095 

099    104    109 

114 

118 

123 

128    133    137 

2 

915 

.96  142 

.96  147  .96  152  .96  156 

.96  161 

.96  166 

.96  171 

.96  175  ..96  180  .96  185 

2 

916 

190 

194    199    204 

209 

213 

218 

223    227    232 

2 

917 

237 

242    246    251 

256 

261 

265 

270    275    280 

3 

918 

284 

289    294    298 

303 

308 

313 

317    322    327 

3 

919 

332 

336   341    346 

350 

355 

360 

365    369    374 

4 

920 

.96  379 

.96  384  .96  388  .96  393 

.96  398 

.96  402 

.96  407 

.96  412  .96  417  .96  421 

5 

921 

426 

431    435    440 

445 

450 

454 

459    464    468 

1 

922 

473 

478    483   487 

492 

497 

501 

506    511    515 

1 

923 

520 

525    530    534 

539 

544 

548 

553    558    562 

2 

924 

567 

572    577   '581 

586 

591 

595 

600    605    609 

2 

925 

.96  614 

.96  619  .96  624  .96  628 

.96  633 

.96  638 

.96  642 

.96  647  .96  652  .96  656 

3 

926 

661 

666    670    675 

680 

685 

689 

694    699    703 

3 

927 

708 

713    717    722 

727 

731 

736 

741    745    750 

4 

928 

755 

759    764    769 

774 

778 

783 

788    792    797 

4 

929 

802 

806   811    816 

820 

825 

830 

834    839    844 

5 

930 

.96  848 

.96  853  .96  858  .96  862 

.96  867 

.96  872 

.96  876 

.96  881  .96  886  .96  890 

4 

931 

895 

900    904    909 

914 

918 

923 

928    932    937 

0 

932 

942 

946    951    956 

960 

965 

970 

974   979   984 

1 

933 

988 

993    997  97  002 

97  007 

97  011 

97  016 

97  021  97  025  97  030 

1 

934 

97  035 

97  039  97  044   049 

053 

058 

063 

067    072    077 

2 

935 

.97  081 

.97  086  .97  090  .97  095 

.97  100 

.97104 

.97  109 

.97  114  .97  118  .97  123 

2 

936 

128 

132    137    142 

146 

151 

155 

160    165    169 

2 

937 

174 

179    183    188 

192 

197 

202 

206    211    216 

3 

938 

220 

225    230    234 

239 

243 

248 

253    257    262 

3 

939 

267 

271    270    280 

285 

290 

294 

299    304    308 

4 

940 

.97  313 

.97  317  .97  322  .97  327 

.97  331 

.97  336 

.97  340 

.97  345  .97  350  .97  354 

5 

941 

359 

364   368   373 

377 

382 

387 

391    396    400 

1 

942 

405 

410    414    419 

424 

428 

433 

437    442    447 

1 

943 

451 

456   460    465 

470 

474 

479 

483    488    493 

2 

944 

497 

502    506    511 

516 

520 

525 

529    534    539 

2 

945 

.97  543 

.97  548  .97  552  .97  557 

.97  562 

.97  566 

.97  571 

.97  575  .97  580  .97  585 

3 

946 

589 

594    598    603 

607 

612 

617 

621    626    630 

3 

947 

635 

640    644    649 

653 

658 

663 

667    672    676 

4 

948 

681 

685    690    695 

699 

704 

708 

713    717    722 

4 

949 

727 

731    736    740 

745 

749 

754 

759   763    768 

5 

950 

N 

.97  772 

.97  777  .97  782  .97  786 

.97  791 

.97  795 

.97  800 

.97  804  .97  809  .97  813 

0 

1     2     3 

4 

5 

6 

7     8     9 

.95  424  — .97  813 


9500-10000 


19 


N 


950 

951 
952 
953 
954 

955 
956 
957 
958 
959 

930 

961 
962 
963 
964 

965 
966 
967 
968 
969 

970 

971 
972 
973 
974 

975 
976 
977 
978 
979 


981 
982 
983 
984 

985 
986 
987 
988 
989 

990 

991 
992 
993 
994 

995 
996 
997 
998 
999 

1000 


N 


Dif. 


.97  772  .97  777  .97  782  .97  786  .97  791 

818    823    827  832  836 

864    868    873  877  882 

909    914    918  923  928 

955    959    964  968  973 

.98  000.  .98  005  .98  009  .98  014  .98  019 

046   050   055  059  064 

091    096    100  105  109 

137    141    146  1.50  .   155 

182    186    191  195  200 

.98  227  .98  232  .98  236  .98  241  .98  245 

272    277    281  286  290 

318    322    327  331  336 

363    367    372  376  381 

408    412    417  421  426 

.98  453  .98  457  .98  462  .98  466  .98  471 

498    502    507  511  516 

"543    547    552  556  561 

588    592    597  601  605 

632    637    641  646  650 

.98677  .98  682  .98  686  .98  691  .98  695 

722    726   731  735  740 

767    771    776  780  784 

811    816    820  825  829 

856    860    865  869  874 

.98  900  .98  905  .98  909  .98  914  .98  918 

945    949    954  958  963 

989    994    998  99  003  99  007 

99  034  99  038  99  043  047  052 

078   083   087  092  096 

.99  123  .99  127  .99  131  .99  136  .99  140 

167    171    176  180  185 

211    216    220  224  229 

255    260    264  269  273 

300  ■  304   308  313  317 

.99  344  .99  348  .99  352  .99  357  .99  361 

388    392    396  401  405 

432    436   441  445  449 

476    480    484  489  493 

520    524    528  533  537 

.99  564  .99  568  .99  572  .99  577  .99  581 

607    612    616  621  625 

651    656    660  664  669 

695    699    704  708  712 

739    743    747  752  756 

.99  782  .99  787  .99  791  .99  795  .99  800 


826 
870 
913 
957 


830 
874 
917 
961 


835  839  843 

878  883  887 

922  926  930 

965  970  974 


.97  795  .97  800  .97  804  .97  809  .97  813 

841  845  850    855    859 

886  891  896   900    905 

932  937  941    946   950 

978  982  987    991    996 

.98  023  .98  028  .98  032  .98  037  .98  041 

068  073  078    082    087 

114  118  123    127    132 

159  164  168    173    177 

204  209  214    218    223 

.98  250  .98  254  .98  259  .98  263  .98  268 

295  299  304    308    313 

340  345  349    354    358 

385  390  394    399   403 

430  435  439   444    448 

.98  475  .98480  .98  484  .98  489  .98  493 

520  525  529    534    538 

565  570  574    579    583 

610  614  619    623    628 

655  659  664    668    673 

.98  700  .98  704  .98  709  .98  713  .98  717 

744  749  753    758    762 

789  793  798   802   807 

834  .  838  843    847    851 

878  883  887   892   896 

.98  923  .98  927  .98  932  .98  936  .98  941 

967  972  976   981    985 

99  012  99  016  99  021  99  025  99  029 

056  061  065    069    074 

100  105  109    114    118 

.99  145  .99  149  .99  154  .99  158  .99  162 

189  193  198'   202    207 

233  238  242    247    251 

277  282  286    291    295 

322  326  330    335    339 

.99  366  .99  370  .99  374  .99  379  .99  383 

410  414  419   423    427 

454  458  463    467    471 

498  502  506    511    515 

542-   546  550    555    559 

.99  585  .99  590  .99  594  .99  599  .99  603 

629  634  638    642    647 

673  677  682    686    691 

717  721  726    730    734 

760  765  769   774   778 

.99  804  .99  808  .99  813  .99  817  .99  822 

848  852  856    861    865 

891  896  900    904    909 

935  939  944    948   952 

978  983  987    991    996 


.00  000  .00  004  .00  009  .00  013  .00  017  .00  022  .00  026  .00  030  .00  035  .00  039 


.97  772 -.99  996 


20 


10000-10500 


N 

0     12     3     4 

5     6     7    8    9 

1000 

.00  000  .00  004  .00  009  .00  013  .00  017 

.00  022  .00  026  .00  030  .00  035  .00  039 

01 

043    048    052    056    061 

065    069    074    078    082 

02 

087    091    095    100    104 

108    113    117    121    126 

03 

130    134    139    143    147 

152    156    160    165    169 

04 

173    178    182    186    191 

195    199    204    208    212 

05 

.00  217  .00  221  .00  225  .00  230  .00  234 

.00  238  .00  243  .00  247  .00  251  .00  255 

06 

260    264    268    273    277 

281    286    290    294    299 

07 

303    307    312    316   320 

325    329    333    337    342 

OS 

346    350    355    359    363 

368    372    376    381    385 

09 

389    393    398    402    406 

411    415    419    424    428 

1010 

.00  432  .00  436  .00  441  .00  445  .00  449 

.00  454  .00  458  .00  462  .00  467  .00  471 

11 

475    479    484    488    492 

497    501    505    509    514 

12 

518    522    527    531    535 

540    544    548    552    557 

13 

561    565    570    574    578 

582    587    591    595    600 

H 

604    608    612    617    621 

625    629    634    638    642 

15 

.00  647  .00  651  .00  655  .00  659  .00  664 

.00  668  .00  672  .00  677  .00  681  .00  685 

16 

689    694    698    702    706 

711    715    719    724    728 

17 

732    736    741    745    749 

753    758    762    766   771 

18 

775    779    783    788    792 

796   800   805    809   813 

19 

817    822    826    830    834 

839    843    847    852    856 

1020 

.00  860  .00  864  .00  869  .00  873  .00  877 

.00  881  .00  886  .00  890  .00  894  .00  898 

21 

903    907    911    915    920 

924    928    932    937    941 

22 

945    949    954    958    962 

966    971    975    979    983 

23 

988    992    996  01000  01005 

01009  01013  01017  01022  01026 

24 

01030  01034  01038    043    047 

051    055    060    064    068 

25 

.01072  .01077  .01081  .01085  .01089 

.01  094  .01  098  .01  102  .01  106  .01  111 

26 

115    119    123    127    132 

136    140    144    149    153 

27 

157    161    166    170    174 

178    182    187    191    195 

28 

199    204    208    212    216 

220    225    229    233    237 

29 

242    246    250    254    258 

263    267    271    275    280 

1030 

.01  284  .01  288  .01  292  .01  296  .01  301 

.01  305  .01  309  .01  313  .01  317  .01  322 

31 

326    330    334    339    343 

347    351    355    360    364 

32 

368   372   376   381    385 

389    393    397    402    406 

33 

410   414    418    423    427 

431    435    439    444    448 

34 

452    456    460    465    469 

473    477    481    486    490 

35 

.01  494  .01  498  .01  502  .01  507  .01  511 

.01  515  .01  519  .01  523  .01  528  .01  532 

36 

536    540    544    549    553 

557    561    565    569   574 

37 

578    582    586    590    595 

599    603    607    611    616 

38 

620    624    628    632    636, 

641    645    649    653    657 

39 

662    666    670    674    678 

682    687    691    695    699 

1040 

.01  703  .01  708  .01  712  .01  716  .01  720 

.01  724  .01  728  .01  733  .01  737  .01  741 

41 

745    749    753    758    762 

766    770    774    778    783 

42 

787    791    795    799   803 

808    812    816    820    824 

43 

828    833    837    841    845 

849    853    858    862    866 

44 

870   874   878   883    887 

891    895    899    903    907 

45 

.01  912  .01  916  .01  920  .01  924  .01  928 

.01  932  .01  937  .01  941  .01  945  .01  949 

46 

953    957    961    966    970 

974    978    982    986    991 

47 

995    999  02  003  02  007  02  011 

02  015  02  020  02  024  02  028  02  032 

48 

.02  036  02  040    044    049    053 

057    061    065    069    073 

49 

078    082    086    090    094 

098    102    107    111    115 

1050 

.02  119  .02  123  .02  127  .02  131  .02  135 

.02  140  .02  144  .02  148  .02  152  .02  156 

N 

0     12     3    4 

5     6^7     8     9 

.00  000  — .02156 


10500-11000  21 


N 

0 

1     2 

3 

4 

5 

6 

7 

8 

9 

1050 

.02  119 

.02123  .02  127 

.02  131 

.02  135 

.02  140 

.02144 

.02  148 

.02  152 

.02  156 

51 

160 

164    169 

173 

177 

181 

185 

189 

193 

197 

52 

202 

206    210 

214 

218 

222 

226 

230 

235 

239 

53 

243 

247    251 

255 

259 

263 

268 

272 

276 

280 

54 

284 

288    292 

296 

301 

305 

309 

313 

317 

321 

55 

.02  325 

.02  329  .02  333 

.02  338 

.02  342 

.02  346 

.02  350 

.02  354 

.02  358 

.02  362 

56 

366 

371    375 

379 

383 

387 

391 

395 

399 

403 

57 

407 

412    416 

420 

424 

428 

432 

436 

440 

444 

58 

449 

453    457 

461 

465 

469 

473 

477 

481 

485 

59 

490 

494    498 

502 

506 

510 

514 

518 

522 

526 

1060 

.02  531 

.02  535  .02  539 

.02  543 

.02  547 

.02  551 

.02  555 

.02  559 

.02  563 

.02  567 

61 

572 

576    580 

584 

588 

592 

596 

600 

604 

608 

62 

612 

617    621 

625 

629 

633 

637 

641 

645 

649 

63 

653 

657    661 

666 

670 

674 

678 

682 

686 

690 

64 

694 

698    702 

706 

710 

715 

719 

723 

727 

731 

65 

.02  735 

.02  739  .02  743 

.02  747 

.02  751 

.02  755 

.02  759 

.02  763 

.02  768 

.02  772 

66 

776 

780    784 

788 

792 

796 

800 

804 

808 

812 

67 

816 

821    825 

829 

833 

837 

841 

845 

849 

853 

68 

857 

861    865 

869 

873 

877 

882 

886 

890 

894 

69 

898 

902    906 

910 

914 

918 

922 

926 

930 

934 

1070 

.02  938 

.02  942  .02  946 

.02  951 

.02  955 

.02  959 

.02  963 

.02  967 

.02  971 

.02  975 

71 

979 

983    987 

991 

995 

999 

03  003 

03  007 

03  011 

03  015 

72 

03  019 

03  024  03  028 

03  032 

03  036 

03  040 

044 

048 

052 

056 

73 

060 

064    068 

072 

076 

080 

084 

088 

092 

096 

74 

100 

104    109 

113 

117 

121 

125 

129 

133 

137 

75 

.03  141 

.03  145  .03  149 

.03  153 

.03  157 

.03  161 

.03  165 

.03  169 

.03  173 

.03  177 

76 

181 

185    189 

193 

197 

201 

205 

209 

214 

218 

77 

222 

226    230 

234 

238 

242 

246 

250 

254 

258 

78 

262 

266    270 

274 

278 

282 

286 

290 

294 

298 

79 

302 

306    310 

314 

318 

322 

326 

330 

334 

338 

1080 

.03  342 

.03  346  .03  350 

.03  354 

.03  358 

.03  362 

.03  366 

.03  371 

.03  375 

.03  379 

81 

383 

387    391 

395 

399 

403 

407 

411 

415 

419 

82 

423 

427    431 

435 

439 

443 

447 

451 

455 

459 

83 

463 

467    471 

475 

479. 

483 

487 

491 

495 

499 

84 

503 

507    511 

515 

519 

523 

527 

531 

535 

539 

85 

.03  543 

.03  547  .03  551 

.03  555 

.03  559 

.03  563 

.03  567 

.03  571 

.03  575 

.03  579 

86 

583 

587    591 

595 

599 

603 

607 

611 

615 

619 

87 

623 

627    631 

635 

639 

643 

647 

651 

655 

659 

88 

663 

667    671 

675 

679 

683 

687 

691 

695 

699 

89 

703 

707    711 

715 

719 

723 

727 

731 

735 

739 

1090 

.03  743 

.03  747  .03  751 

.03  755 

.03  759 

.03  763 

.03  767 

.03  771 

.03  775 

.03  778 

91 

782 

786    790 

794 

798 

802 

806 

810 

814 

818 

92 

822 

826    830 

834 

838 

842 

846 

850 

854 

858 

93 

862 

866   870 

874 

878 

882 

886 

890 

894 

898 

94 

902 

906    910 

914 

918 

922 

926 

930 

933 

937 

95 

.03  941 

.03  945  .03  949 

.03  953 

.03  957 

.03  961 

.03  965 

.03  969 

.03  973 

.03  977 

96 

981 

985    989 

993 

997 

04  001 

04  005 

04  009 

04  013 

04  017 

97 

04  021 

04  025  04  029 

04  033 

04  036 

040 

044 

048 

052 

056 

98 

060 

064    068 

072 

076 

080 

084 

088 

092 

096 

99 

100 

104    108 

112 

116 

120 

123 

127 

131 

135 

1100 

.04  139 
0 

.04  143  .04147 

.04  151 

.04  155 

.04  159 

.04  163 

.04  167 

.04  171 

.04175 
9  . 

N 

1     2 

3 

4 

5 

6 

7 

8 

,02 119 -.04 175 


22 


TABLE  II 

IMPORTANT  CONSTANTS  AND  THEIR  COMMON  LOGARITHMS 


The  circumference  of  a  circle      .     .     .     .     =           360°    .  . 

=       21600'    .  . 

=  1  296  000"  .  . 

7r  =  3.  14  159  265  358  979  323  846  264  338  328 

7r2 =9. 86  960  440  . 

I/tt ■.     .     =0.31830  989  . 

l/7r2 =0.10132  118  . 

Vtt =  1.  77  245  385  . 

I/Vtt =0.56  418  958  . 

\/(3/7r) =0.97  720  502  . 

y(4/7r) =  1.12  837  917  . 

^TT =1.46  459189  . 

I/a^tt =0.68  278  406  . 

1  radian  =  ISOVtt =  57.  29  577  951° 

=  3  437.74  677'  . 

=  206  264.  806"  . 

=  0.  01  745  329  . 

=  0.  00  029  089  . 

=  0.  00  000  485  . 

=  2.  71  828  183  . 

=  0.43  429  448  . 

=  2.30  258  5  .     . 
=  39.37  inches     . 
=  1.09  361  1  yard 
=  3.28  083  3  feet 
=  0.62  137  0  mile 


In  terms  of  a  radian 1° 

V 
V 
Base  of  natural  logarithms  =  e  .  .  .  . 
Modulus  of  common  logarithms  =  logioe  . 
Factor  by  which  to  multiply  common  logs, 
to  obtain  natural  logs,  or  1/logio  e  .  . 
1  meter . 


1  kilometer 

1  mile =  1.60  934  7  kilom. 

1  yard =  0.91  440  2  metre 

1  foot =  0.30  480  1  metre 

1  inch =  25.40  005  mm. 

1  pound  Av.     . =  7000  grains 

=  453.59  242  77  grammes 

1  ounce  Av =  28.34  953  grammes 

1  ounce  Troy =  31.10  348  grammes 

1  grain " =  0.06  479  892  gramme 


2.20  462  2  pounds  Av. 
15.43  235  639  grains 


1  kilogramme 

1  gramme 

1  litre =  1.05  668  U.  S.  quart 

=  0.26417  U.  S.  gallon 
=  33.814  U.  S.  fluid  oz 

1  quart,  U.  S =  0.94  636  litre 


1  gallon,  U.  S. 
1  fluid  ounce    . 
1  gallon  U.  S. 
1  British  gallon 
1  British  bushel 


=  3.78  544  litres  . 
=  0.02  957  3  litre 
=  231  cu.  inches 
=  4.54  346  litres  . 
=  36.34  77  litres  . 


Common  Logarithms 

2.  55  630  250 
4.  ZZ  445  375 
6.  11  260  500 
0.  49  714  987 

0.  99  429  975 

1.  50  285  013 
1.00  570  025 

0.  24  857  494 

1.  75  142  506 
1.98  998  569 
0.  05  245  506 

0.  16  571  662 
1.83  428  338 

1.  75  812  263 

3.  SZ  e>l1  388 
5.31442  513 

2.  24  187  737 

6.68  557  487 
0.  43  429  448 
1.63  778  431 

0.36  22157 
1.59  516  54 

0.  03  886  29 
0.51598  42 

1.  79  335  03 

0.  20  664  97 
1.96113  71 

1.  48  401  58 

1.  40  483  46 

3.  84  509  80 

2.  65  666  58 
1.45  254  59 
1.  49  280  91 
2.81  156  78 

0.  34  ZZZ  42 

1.  18  843  22 
0.  02  394  4 
1.42  188  4 
1.52  910 
1.97  605  6 
0.57  8116 

2.  47  090 

2.  36  361  20 

0.  65  738  67 

1.  56  047  69 


23 


TABLE  m 


THE  COMMOI^  LOaARITHMS 


OF  THE 


TRIGONOMETRIC  FUNCTIONS   OF  ANGLES 


From  1°  to  89° 

FOR  EVERY  MINUTE 


FIVE-PLACE  MANTISSAS 


24 

1° 

f 

log  sin  log  tan  log  cot  log  cos 

1 

8-10   8-10    1   9-10 

0 

.24  186  .24  192  .75  808  .99  993 

60 

1 

903    910   090    993 

59 

2 

25  609  25  616  74  384    993 

58 

3 

26  304  26  312  73  688   993 

57 

4 

988    996   004    992 

56 

5 

.27  661  .27  669  .72  331  .99  992 

55 

6 

28  324  28  332  71668    992 

54 

7 

977    986   014    992 

53 

8 

29  621  29  629  70  371    992 

52 

9 

30  255  30  263  69  737    991 

51 

10 

.30  879  .30  888  .69112  .99  991 

50 

11 

31495  31505  68  495    991 

49 

12 

32  103  32  112  67  888    990 

48 

13 

702    711    289    990 

47 

14 

33  292  33  302  66  698    990 

46 

15 

.33  875  .33  886  .66  114  .99  990 

45 

16 

34  450  34  461  65  539    989 

44 

17 

35  018  35  029  64  971    989 

43 

18 

578    590   410   989 

42 

19 

36131  36143  63  857    989 

41 

20 

.36  678  .36  689  .63  311  .99  988 

40 

21 

37  217  37  229  62  771    988 

39 

22 

750    762    238    988 

38 

23 

38  276  38  289  61711    987 

37 

24 

796    809    191    987 

36 

25 

.39  310  .39  323  .60  677  .99  987 

35 

26 

818    832    168    986 

34 

27 

40  320  40  334  59  666   986 

33 

28 

816    830    170    986 

32 

29 

41307  41321  58  679    985 

31 

30 

.41  792  .41  807  .58  193  .99  985 

30 

31 

42  272  42  287  57  713    985 

29 

32 

746    762    238    984 

28 

33 

43  216  43  232  56  768    984 

27 

34 

680    696    304    984 

26 

35 

.44  139  .44  156  .55  844  .99  983 

25 

36 

594    611    389    983 

24 

37 

45  044  45  061  54  939    983 

23 

38 

489    507    493    982 

22 

39 

930   948    052    982 

21 

40 

.46  366  .46  385  .53  615  .99  982 

20 

41 

799    817    183    981 

19 

42 

47  226  47  245  52  755    981 

18 

43 

650    669    331    981 

17 

44 

48  069  48  089  51911    980 

16 

45 

.48  485  .48  505  .51495  .99  980 

15 

46 

896   917   083   979 

14 

47 

49  304  49  325  50  675    979 

13 

48 

708    729    271    979 

12 

49 

50108  50130  49  870   978 

11 

50 

.50  504  .50  527  .49  473  .99  978 

10 

51 

897    920    080   977 

9 

52 

51287  51310  48  690   977 

8 

53 

673    696   304    977 

7 

54 

52  055  52  079  47  921    976 

6 

55 

.52  434  .52  459  .47  541  .99  976 

5 

56 

810    835    165    975 

4 

57 

53  183  53  208  46  792    975 

3 

58 

552    578    422    974 

2 

59 

919   945    055    974 

1 

60 

.54  282  .54  308  .45  692  .99  974 
8-10  8-10    1   9-10 

0 

f 

log  cos  log  cot  log  tan  log  sin 

f 

2° 


f 

log  sin  log  tan  log  cot  log  cos 

f 

8-10   8-10    1   9-10 

0 

.54  282  .54  308  .45  692  .99  974 

60 

1 

642    669    331    973 

59 

2 

999  55  027  44  973    973 

58 

3 

55  354    382    618    972 

57 

4 

705    734    266   972 

56 

5 

.56  054  .56  083  .43  917  .99  971 

55 

6 

400    429    571    971 

54 

7 

743    773    227    970 

53 

8 

57  084  57  114  42  886   970 

52 

9 

421    452    548    969 

51 

10 

.57  757  .57  788  .42  212  .99  969 

50 

11 

58  089  58121  41879    968 

49 

12 

419    451    549    968 

48 

13 

747    779    221    967 

47 

14 

59  072  59  105  40  895    967 

46 

15 

.59  395  .59  428  .40  572  .99  967 

45 

16 

715    749    251    966 

44 

17 

60  033  60  068  39  932    966 

43 

18 

349    384    616    965 

42 

19 

662    698    302    964 

41 

20 

.60  973  .61  009  .38  991  .99  %4 

40 

21 

61282    319    681    963 

39 

22 

589    626    374    963 

38 

23 

894    931    069    962 

37 

24 

62  196  62  234  37  766   962 

36 

25 

.62  497  .62  535  .37  465  .99  961 

35 

26 

795    834    166    961 

34 

27 

63  091  63  131  36  869    960 

33 

28 

385    426    574   .960 

32 

29 

678    718    282    959 

31 

30 

.63  968  .64  009  .35  991  .99  959 

30 

31 

64  256    298    702    958 

29 

32 

543    585    415    958 

28 

33 

827    870    130   957 

27 

34 

65  110  65  154  34  846    956 

26 

35 

.65  391  .65  435  .34  565  .99  956 

25 

36 

670    715    285    955 

24 

37 

947    993    007    955 

23 

38 

66  223  66  269  33  731    954 

22 

39 

497    543    457    954 

21 

40 

.66  769  .66  816  .33  184  .99  953 

20 

41 

67  039  67  087  32  913    952 

19 

42 

308    356    644    952 

18 

43 

575    624   376    951 

17 

44 

841    890    110    951 

16 

45 

.68104  .68154  .31846  .99  950 

15 

46 

367   417    583   949 

14 

47 

627    678    322    949 

13 

48 

886    938    062    948 

12 

49 

69144  69196  30  804    948 

11 

50 

.69  400  .69  453  .30  547  .99  947 

10 

51 

654    708    292    946 

9 

52 

907    962    038    946 

8 

53 

70159  70  214  29  786    945 

7 

54 

409    465    535    944 

6 

55 

.70  658  .70  714  .29  286  .99  944 

5 

56 

905    962    038    943 

4 

57 

71151  71208  28  792    942 

3 

58 

395    453    547    942 

2 

59 

638    697    303    941 

1 

60 

t 

.71880  .71940  .28  060  .99  940 
8-10   8-10    1   9-10 
log  cos  log  cot  log  tan  log  sin 

0 

t 

88' 


87° 


3° 

t 

log  sin  log  tan  log  cot  log  cos 

f 

8-10   8-10    1    9-10 

0 

.71880  .71940  .28  060  .99  940 

60 

1 

72  120  72  181  27  819    940 

59 

2 

359    420    580    939 

58 

3 

597    659    341    938 

57 

4 

834    896    104   938 

56 

5 

.73  069  .73  132  .26  868  .99  937 

55 

6 

303    366    634    936 

54 

7 

535    600    400    936 

53 

8 

767    832    168    935 

52 

9 

997  74  063  25  937    934 

51 

10 

.74  226  .74  292  .25  708  .99  934 

50 

11 

454    521    479   933 

49 

12 

680    748    252    932 

48 

13 

906   974    026    932 

47 

14 

75  130  75  199  24  801    931 

46 

15 

.75  353  .75  423  .24  577  .99  930 

45 

16 

575    645    355    929 

44 

17 

795    867    133    929 

43 

18 

76  015  76  087  23  913    928 

42 

19 

231    306    694    927 

41 

20 

.76  451  .76  525  .23  475  .99  926 

40 

21 

667    742    258    926 

39 

22 

883    958    042    925 

38 

23 

77  097  77  173  22  827    924 

37 

24 

310    387    613    923 

36 

25 

.77  522  .77  600  .22  400  .99  923 

35 

26 

733    811    189    922 

34 

27 

943  78  022  21978    921 

33 

28 

78152    232    768    920 

32 

29 

360    441    559    920 

31 

30 

.78  568  .78  649  .21351  .99  919 

30 

31 

774   855    145    918 

29 

32 

979  79  061  20  939    917 

28 

33 

79183    266    734    917 

27 

34 

386    470    530    916 

26 

35 

.79  588  .79  673  .20  327  .99  915 

25 

36 

789    875    125    914 

24 

37 

990  80  076  19  924    913 

23 

38 

80  189    277    723    913 

22 

39 

388    476    524    912 

21 

40 

.80  585  .80  674  .19  326  .99  911 

20 

41 

782    872    128    910 

19 

42 

978  81068  18  932    909 

18 

43 

81173    264    736    909 

17 

44 

367    459    541    908 

16 

45 

.81  560  .81  653  .18  347  .99  907 

15 

46 

752    846    154    906 

14 

47 

944  82  038  17  962    905 

13 

48 

82  134   230    770   904 

12 

49 

324    420    580    904 

11 

50 

.82  513  .82  610  .17  390  .99  903 

10 

51 

701    799    201    902 

9 

52 

888   987   013    901 

8 

53 

83  075  83  175  16  825    900 

7 

54 

261    361    639    899 

6 

55 

.83  446  .83  547  .16  453  .99  898 

5 

56 

630    732    268    898 

4 

57 

813    916    084    897 

3 

58 

996  84  100  15  900    896 

2 

59 

84  177    282    718    895 

1 

60 
f 

.84  358  .84  464  .15  536  .99  894 
8-10  8-10    1   9-10 
log  cos  log  cot  log  tan  log  sin 

0 

f 

25 


10 

11 

12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
.60 


log  sin  log  tan  log  cot  log  cos 


8-10   8-10 

.84  358  .84  464 


539 
718 


646 
826 


897  85  006 


85  075 

.85  252 
429 
605 
780 
955 

.86  128 
301 
474 
645 
816 

.86  987 

87  156 
325 
494 
661 

.87  829 
995 

88161 
326 
490 

.88  654 
817 
980 

89142 
304 

.89  464 
625 
784 
943 

90102 

.90  260 
417 
574 
730 
885 

.91  040 
195 
349 
502 
655 

.91  807 
959 

92  110 
261 
411 

.92  561 
710 
859 

93  007 
154 

.93  301 
448 
594 
740 
885 

.94  030 
8-10 

log  cos 


185 

.85  363 
540 
717 
893 

86  069 

.86  243 
417 
591 
763 
935 

.87  106 
277 
447 
616 
785 

.87  953 

88  120 
287 
453 
618 

.88  783 
948 

89111 
274 
437 

.89  598 
760 
920 

90  080 
240 

.90  399 

557 

715 

872 

91029 

.91 185 
340 
495 
650 
803 

.91  957 

92  110 
262 
414 
565 

.92  716 
866 

93  016 
165 
313 

.93  462 
609 
756 
903 

94  049 
.94  195 

8-10 
log  cot 


1   9-10 

.15  536  .99  894 
354  893 
174    892 

14  994  891 
815    891 

.14  637  .99  890 
460  889 
283  888 
107    887 

13  931    886 

.13  757  .99  885 
583  884 
409  883 
237  882 
065    881 


12  894  , 
723 

553 
384 
215 
.12  047 
11880 
713 
547 
382 

.11217 
052 

10  889 
726 
563 

.10  402 
240 
080 

09  920 
760 

.09  601 
443 
285 
128 

08  971 

.08  815 
660 
505 
350 
197 

.08  043 

07  890 
738 
586 
435 

.07  284 
134 

06  984 
835 
687 

.06  538 
391 
244 
097 

05  951 

.05  805 
1 

log  tan 


.99  880 
879 
879 

878 
877 
.99  876 
875 
874 
873 
872 

.99  871 
870 
869 
868 
867 

.99  866 
865 
864 
863 
862 

.99  861 
860 
859 
858 
857 

.99  856 
855 
854 
853 
852 

.99  851 
850 
848 
847 
846 

.99  845 
844 
843 
842 
841 

.99  840 
839 
838 
837 
836 

.99  834 
9-10 
log  sin 


86< 


85' 


26 

5° 

r 

log  sin  log  tan  log  cot  log  cos 

f 

8-10   8-10    1   9-10 

0 

.94  030  .94  195  .05  805  .99  834 

60 

1 

174    340    660    833 

59 

2 

317    485    515    832 

58 

3 

461    630    370   831 

57 

4 

603    773    227    830 

56 

5 

.94  746  .94  917  .05  083  .99  829 

55 

6 

887  95  060  04  940    828 

54 

7 

95  029    202    798    827 

53 

8 

170    344    656    825 

52 

9 

310   486    514    824 

51 

10 

.95  450  .95  627  .04  373  .99  823 

50 

11 

589    767    233    822 

49 

12 

728    908    092    821 

48 

13 

867  96  047  03  953    820 

47 

14 

96  005    187   813   819 

46 

15 

.96  143  .96  325  .03  675  .99  817 

45 

16 

280    464    536    816 

44 

17 

417    602    398    815 

43 

18 

553    739    261    814 

42 

19 

689    877    123    813 

41 

20 

.96  825  .97  013  .02  987  .99  812 

40 

21 

960    150    850   810 

39 

22 

97  095    285    715    809 

38 

23 

229    421    579    808 

37 

24 

363    556    444    807 

36 

25 

.97  496  .97  691  .02  309  .99  806 

35 

26 

629    825    175    804 

34 

27 

762    959    04]    803 

33 

28 

894  98  092  01908    802 

32 

29 

98  026   225    775    801 

31 

30 

.98  157  .98  358  .01  642  .99  800 

30 

31 

288    490    510    798 

29 

32 

419    622    378    797 

28 

33 

549   753    247    796 

27 

34 

679   884    116    795 

26 

35 

.98  808  .99  015  .00  985  .99  793 

25 

36 

937    145    855    792 

24 

37 

99  066   275    725    791 

23 

38 

194   405    595    790 

22 

39 

322    534    466    788 

21 

40 

.99  450  .99  662  .00  338  .99  787 

20 

41 

577    791    209    786 

19 

42 

704    919    081    785 

18 

43 

830  00  046  99  954    783 

17 

44 

956    174    826    782 

16 

45 

.00  082  .00  301  .99  699  .99  781 

15 

46 

207   427    573    780 

14 

47 

332   553   447    778 

13 

48 

456   679   321    777 

12 

49 

581    805    195    776 

11 

50 

.00  704  .00  930  .99  070  .99  775 

10 

51 

828  0105i  98  945    773 

9 

52 

951    179    821    772 

8 

53 

01074    303    697    771 

7 

54 

196    427    573    769 

6 

55 

.01318  .01550  .98  450  .99  768 

5 

56 

440    673    327    767 

4 

57 

561    796    204    765 

3 

58 

682    918    082    764 

2 

59 

803  02  040  97  960    763 

1 

60 

.01923  .02  162  .97  838  .99  761 
9-10  9-10   0   9-10 
log  cos  log  cot  log  tan  log  sin 

0 

t 

6° 

f 

log  sin 

log  tan  log  cot 

log  cos 

t 

9-10 

9-10   0 

9-10 

0 

.01  923 

.02  162  .97  838 

.99  761 

60 

1 

02  043 

283    717 

760 

59 

2 

163 

404    596 

759 

58 

3 

283 

525    475 

757 

57 

4 

402 

645    355 

756 

56 

5 

.02  520 

.02  766  .97  234 

.99  755 

55 

6 

639 

885    115 

753 

54 

7 

757 

03  005  96  995 

752 

53 

8 

874 

124    876 

751 

52 

9 

992 

242    758 

749 

51 

10 

.03  109 

.03  361  .96  639 

.99  748 

50 

11 

226 

479    521 

747 

49 

12 

342 

597    403 

745 

48 

13 

458 

714    286 

744 

47 

14 

574 

832    168 

742 

46 

15 

.03  690 

.03  948  .96  052 

.99  741 

45 

16 

805 

04  065  95  935 

740 

44 

17 

920 

181    819 

738 

43 

18 

04  034 

297    703 

737 

42 

19 

149 

413    587 

736 

41 

20 

.04  262 

.04  528  .95  472 

.99  734 

40 

21 

376 

643    357 

733 

39 

22 

490 

758    242 

731 

38 

23 

603 

873    127 

730 

37 

24 

715 

987    013 

728 

36 

25 

.04  828 

.05  101  .94  899 

.99  727 

35 

26 

940 

214    786 

726 

34 

27 

05  052 

328   672 

724 

33 

28 

164 

441    559 

723 

32 

29 

275 

553    447 

721 

31 

30 

.05  386 

.05  666  .94  334 

.99  720 

30 

31 

497 

778    222 

718 

29 

32 

607 

890    110 

717 

28 

33 

717 

06  002  93  998 

716 

27 

34 

827 

113   887 

714 

26 

35 

.05  937 

.06  224  .93  776 

.99  713 

25 

36 

06  046 

335    665 

711 

24 

37 

155 

445    555 

710 

23 

38 

264 

556    444 

708 

22 

39 

372 

666    334 

707 

21 

40 

.06  481 

.06  775  .93  225 

.99  705 

20 

41 

589 

885    115 

704 

19 

42 

696 

994    006 

702 

18 

43 

804 

07103  92  897 

701 

17 

44 

911 

211    789 

699 

16 

45 

.07  018 

.07  320  .92  680 

.99  698 

15 

46 

124 

428    572 

696 

14 

47 

231 

536    464 

695 

13 

48 

337 

643    357 

693 

12 

49 

442 

751    249 

692 

11 

50 

.07  548 

.07  858  .92  142 

.99  690 

10 

51 

653 

964    036 

689 

9 

52 

758 

08  071  91929 

687 

8 

53 

863 

177    823 

686 

7 

54 

968 

283    717 

684 

6 

55 

.08  072 

.08  389  .91611 

.99  683 

5 

56 

176 

495    505 

681 

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14^ 

log  sin  log  tan  log  cot 
9-10  9-10   0 

.38  368  .39  677  .60  323 
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670  999  001 
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921  266  734 
971    319    681 

39  021  372  628 
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730 
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9-10 

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9-10 

log  cot 


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100 
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943 
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839 
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0 

log  tan 


log  COS 

f 

9-10 

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23 

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20 

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18 

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9 

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4 

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3 

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2 

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0 

9-10 

log  sin 

f 

76< 


75° 


15° 


1 

log  sin  log  tan  log  cot  log  cos 

1 

9-10   9-10    0   9-10 

0 

.41  300  .42  805  .57  195  .98  494 

60 

1 

347    856    144    491 

59 

2 

394    906    094    488 

58 

3 

441    957    043    484 

57 

4 

488  43  007  56  993    481 

56 

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.41535  .43  057  .56  943  .98  477 

55 

6 

582    108    892    474 

54 

7 

628    158    842    471 

53 

8 

675    208    792    467 

52 

9 

722    258    742    464 

51 

10 

.41  768  .43  308  .56  692  .98  460 

50 

11 

815    358    642    457 

49 

12 

861    408    592    453 

48 

13 

908    458    542    450 

47 

14 

954    508    492    447 

46 

15 

.42  001  .43  558  .56  442  .98  443 

45 

16 

047    607    393    440 

44 

17 

093    657    343    436 

43 

18 

140    707    293    433 

42 

19 

186    756    244    429 

41 

20 

.42  232  .43  806  .56  194  .98  426 

40 

21 

278    855    145    422 

39 

22 

324    905    095    419 

38 

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370    954    046    415 

37 

24 

416  44  004  55  996   412 

36 

25 

.42  461  .44  053  .55  947  .98  409 

35 

26 

507    102    898    405 

34 

27 

553    151    849    402 

33 

28 

599    201    799    398 

32 

29 

644    250    750    395 

31 

30 

.42  690  .44  299  .55  701  .98  391 

30 

31 

735    348    652    388 

29 

32 

781    397    603    384 

28 

33 

826    446    554    381 

27 

34 

872    495    505    377 

26 

35 

.42  917  .44  544  .55  456  .98  373 

25 

36 

962    592    408    370 

24 

37 

43  008    641    359    366 

23 

38 

053    690    310    363 

22 

39 

098    738    262    359 

21 

40 

.43  143  .44  787  .55  213  .98  356 

20 

41 

188    836    164    352 

19 

42 

233    884    116    349 

18 

43 

278    933    067    345 

17 

44 

323    981    019    342 

16 

45 

.43  367  .45  029  .54  971  .98  338 

15 

46 

412    078    922    334 

14 

47 

457    126    874    331 

13 

48 

502    174    826    327 

12 

49 

546    222    778    324 

11 

50 

.43  591  .45  271  .54  729  .98  320 

10 

51 

635    319    681    317 

9 

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680    367    633    313 

8 

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724    415    585    309 

7 

54 

769    463    537    306 

6 

55 

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5 

56 

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4 

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901    606    394    295 

3 

58 

946    654    346    291 

2 

59 

990    702    298    288 

1 

60 

.44  034  .45  750  .54  250  .98  284 
9-10  9-10   0   9-10 

0 

f 

log  cos  log  cot  log  tan  log  sin 

f 

16° 

31 

t 

log  sin  log  tan  log  cot  log  cos 
9-10  9-10   0   9-10 

1 

0 

.44  034  .45  750  .54  250  .98  284 

60 

1 

078    797    203    281 

59 

2 

122    845    155    277 

58 

3 

166    892    108    273 

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4 

210    940    060    270 

56 

5 

.44  253  .45  987  .54  013  .98  266 

55 

6 

297  46  035  53  965    262 

54 

7 

341    082    918    259 

53 

8 

385    130    870    255 

52 

9 

428    177    823    251 

51 

10 

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50 

11 

516    271    729    244 

49 

12 

559    319    681    240 

48 

13 

602    366    634    237 

47 

14 

646    413    587    233 

46 

15 

.44  689  .46  460  .53  540  .98  229 

45 

16 

733    507    493    226 

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43 

18 

819    601    399    218 

42 

19 

862    648    352    215 

41 

20 

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40 

21 

948    741    259    207 

39 

22 

992    788    212    204 

38 

23 

45  035    835    165    200 

37 

24 

077    881    119    196 

36 

25 

.45  120  .46  928  .53  072  .98  192 

35 

26 

163   975    025    189 

34 

27 

206  47  021  52  979    185 

33 

28 

249    068    932    181 

32 

29 

292    114   886   177 

31 

30 

.45  334  .47  160  .52  840  .98  174 

30 

31 

377   207    793    170 

29 

32 

419    253    747    166 

28 

33 

462    299    701    162 

27 

34 

504    346    654    159 

26 

35 

.45  547  .47  392  .52  608  .98155 

25 

36 

589    438    562    151 

24 

37 

632    484    516    147 

23 

38 

674    530    470    144 

22 

39 

716   576   424    140 

21 

40 

.45  758  .47  622  .52  378  .98136 

20 

41 

801    668    332    132 

19 

42 

843    714    286    129 

18 

43 

885    760    240    125 

17 

44 

927    806    194    121 

16 

45 

.45  969  .47  852  .52  148  .98117 

15 

46 

46011    897    103    113 

14 

47 

053    943    057    110 

13 

48 

095    989   on    106 

12 

49 

136  48  035  51965    102 

11 

50 

.46178  .48  080  .51920  .98  098 

10 

51 

220    126    874    094 

9 

52 

262    171    829    090 

8 

53 

303   217    783    087 

7 

54 

345    262    738    083 

6 

55 

.46  386  .48  307  .51693  .98  079 

5 

56 

428    353    647    075 

4 

57 

469    398    602    071 

3 

58 

511    443    557    067 

2 

59 

552    489    511    063 

1 

60 

.46  594  .48  534  .51  466  .98  060 
9-10  9-10   0   9-10 

0 

1 

log  cos  log  cot  log  tan  log  sin 

f 

74c 


73° 


32 

17° 

f 

log  sin  log  tan  log  cot 

log  cos 

f 

9-10   9-10    0 

9-10 

0 

.46  594  .48  534  .51466 

.98  060 

60 

1 

635    579    421 

056 

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2 

676    624    376 

052 

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3 

717    669    331 

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4 

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6 

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036 

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923    894    106 

029 

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9 

964    939    061 

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11 

045  49  029  50  971 

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086-   073    927 

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127    118    882 

009 

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168    163    837 

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249    252    748 

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17 

290    296    704 

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18 

330    341    659 

989 

42 

19 

371  9    385    615 

986 

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20 

.47  411  .49  430  .50  570 

.97  982 

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21 

452    474    526 

978 

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22 

492    519    481 

974 

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533    563    437 

970 

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573   607   393 

966 

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.47  613  .49  652  .50  348 

.97  962 

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654    696    304 

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27 

694    740    260 

954 

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28 

734    784    216 

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774    828    172 

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.47  814  .49  872  .50  128 

.97  942 

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854    916    084 

938 

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934 

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934  50  004  49  996 

930 

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054    136    864 

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133    223    777 

910 

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173    267    733 

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20 

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252    355    645 

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292    398    602 

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332    442    558 

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371    485    515 

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15 

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450    572    428 

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870 

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568   703    297 

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.48  998  .51178  .48  822 

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9-10  9-10   0 

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log  cos  log  cot  log  tan 

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.63  662  .68  174  .31  826  .95  488 

20 

41 

689    206    794    482 

19 

42 

715    239   761    476 

18 

43 

741    271    729    470 

17 

44 

767    303    697    464 

16 

45 

.63  794  .68  336  .31  664  .95  458 

15 

46 

820    368    632    452 

14 

47 

846   400    600   446 

13 

48 

872    432    568    440 

12 

49 

898   465    535   434 

11 

60 

.63  924  .68  497  .31  503  .95  427 

10 

51 

950    529   471    421 

9 

52 

976    561    439   415 

8 

53 

64  002    593    407    409 

7 

54 

028    626    374    403 

6 

55 

.64  054  .68  658  .31342  .95  397 

5 

56 

080    690    310    391 

4 

57 

106    722    278    384 

3 

58 

132    754    246    378 

2 

59 

158    786    214    372 

1 

60 

.64  184  .68  818  .31  182  .95  366 
9-10  9-10   0   9-10 

0 

t 

log  cos  log  cot  log  tan  log  sin 

f 

26° 


1 

log  sin  log  tan  log  cot  log  cos 

f 



9-10   9-10   0   9-10 

0 

.64  184  .68  818  .31  182  .95  366 

60 

1 

210    850    150    360 

59 

2 

236    882    118    354 

58 

3 

262    914    086    348 

57 

4 

288    946   054    341 

56 

5 

.64  313  .68  978  .31022  .95  335 

55 

6 

339  69  010  30  990    329 

54 

7 

365    042    958    323 

53 

8 

391    074    926    317 

52 

9 

417    106    894    310 

51 

10 

.64  442  .69  138  .30  862  .95  304 

50 

11 

468    170    830    298 

49 

12 

494    202    798    292 

48 

13 

519    234    766    286 

47 

14 

545    266    734    279 

46 

15 

.64  571  .69  298  .30  702  .95  273 

45 

16 

596   329    671    267 

44 

17 

622    361    639    261 

43 

18 

647    393    607    254 

42 

19 

673    425    575    248 

41 

20 

.64  698  .69  457  .30  543  .95  242 

40 

21 

724    488    512    236 

39 

22 

749    520    480    229 

38 

23 

775    552    448    223 

37 

24 

800    584    416    217 

36 

25 

.64  826  .69  615  .30  385  .95  211 

35 

26 

851    647    353    204 

34 

27 

877    679    321    198 

33 

28 

902    710    290    192 

32 

29 

927    742    258    185 

31 

30 

.64  953  .69  774  .30  226  .95  179 

30 

31 

978    805    195    173 

29 

32 

65  003    837    163    167 

28 

33 

029    868    132    160 

27 

34 

054    900    100    154 

26 

35 

.65  079  .69  932  .30  068  .95  148 

25 

36 

104    963    037    141 

24 

37 

130    995    005    135 

23 

38 

155  70  026  29  974    129 

22 

39 

180    058    942    122 

21 

40 

.65  205  .70  089  .29  911  .95  116 

20 

41 

230    121    879    110 

19 

42 

255    152    848    103 

18 

43 

281    184    816   097 

17 

44 

306    215    785    090 

16 

45 

.65  331  .70  247  .29  753  .95  084 

16 

46 

356    278    722    078 

14 

47 

381    309    691    071 

13 

48 

406    341    659    065 

12 

49 

431    372    628   059 

U 

50 

.65  456  .70  404  .29  596  .95  052 

10 

51 

481    435    565    046 

9 

52 

506   466    534    039 

8 

53 

531    498    502    033 

7 

54 

556    529   471  .  027 

6 

55 

.65  580  .70  560  .29  440  .95  020 

6 

56 

605    592    408    014 

4 

57 

630    623    377    007 

3 

58 

655    654   346    001 

2 

59 

680    685    315  94  995 

1 

60 

.65  705  .70  717  .29  283  .94  988 
9-10   9-10    0   9-10 

0 

t 

log  cos  log  cot  log  tan  log  sin 

f 

64° 


63^ 


2T 


) 

log  sin  log  tan  log  cot  log  cos 
9-10   9-10    0   9-10 

1 

0 

.65  705  .70  717  .29  283  .94  988 

60 

1 

729    748    252    982 

59 

2 

754    779    221    975 

58 

3 

779    810    190    969 

57 

4 

804    841    159    962 

56 

5 

.65  828  .70  873  .29  127  .94  956 

55 

6 

853    904    096    949 

54 

7 

878    935    065    943 

53 

8 

902    966    034    936 

52 

9 

927    997    003    930 

51 

10 

.65  952  .71028  .28  972  .94  923 

50 

11 

976   059    941    917 

49 

12 

66  001    090    910    911 

48 

13 

025    121    879    904 

47 

14 

050    153    847    898 

46 

15 

.66  075  .71  184  .28  816  .94  891 

45 

16 

099    215    785    885 

44 

17 

124    246    754    878 

43 

18 

148    277    723    871 

42 

19 

173    308    692    865 

41 

20 

.66  197  .71  339  .28  661  .94  858 

40 

21 

221    370    630    852 

39 

22 

246   401    599    845 

38 

23 

270    431    569    839 

37 

24 

295    462    538    832 

36 

25 

.66  319  .71493  .28  507  .94  826 

35 

26 

343    524    476    819 

34 

27 

368    555    445    813 

33 

28 

392    586    414    806 

32 

29 

416    617    383    799 

31 

30 

.66  441  .71  648  .28  352  .94  793 

30 

31 

465    679    321    786 

29 

32 

489    709    291    780 

28 

33 

513    740    260    773 

27 

34 

537    771    229    767 

26 

35 

.66  562  .71  802  .28  198  .94  760 

25 

36 

586    833    167    753 

24 

37 

610    863    137    747 

23 

38 

634    894    106    740 

22 

39 

658    925    075    734 

21 

40 

.66  682  .71  955  .28  045  .94  727 

20 

41 

706    986    014    720 

19 

42 

731  72  017  27  983    714 

18 

43 

755    048    952    707 

17 

44 

779    078    922    700 

16 

45 

.66  803  .72  109  .27  891  .94  694 

15 

46 

827    140    860    687 

14 

47 

851    170    830    680 

13 

48 

875    201    799    674 

12 

49 

899    231    769    667 

11 

50 

.66  922  .72  262  .27  738  .94  660 

10 

51 

946    293    707    654 

9 

52 

970    323    677    647 

8 

53 

994    354    646    640 

7 

54 

67  018    384    616    634 

6 

55 

.67  042  .72  415  .27  585  .94  627 

5 

56 

066    445    555    620 

4- 

57 

090    476    524    614 

3 

58 

113    506    494    607 

2 

59 

137    537    463    600 

1 

60 

f 

.67  161  .72  567  .27  433  .94  593 
9-10   9-10   0   9-10 
log  cos  log  cot  log  tan  log  sin 

0 

1 

28° 

37 

t 

log  sin  log  tan  log  cot 

log  cos 

1 

9-10   9-10    0 

9-10 

0 

.67  161  .72  567  .27  433 

.94  593 

60 

1 

185    598    402 

587 

59 

2 

208    628    372 

580 

58 

3 

232    659    341 

573 

57 

4 

256    689    311 

567 

56 

5 

.67  280  .72  720  .27  280 

.94  560 

55 

6 

303    750    250 

553 

54 

7 

327    780    220 

546 

53 

8 

350    811    189 

540 

52 

9 

374    841    159 

533 

51 

10 

.67  398  .72  872  .27  128 

.94  526 

50 

11 

421    902    098 

519 

49 

12 

445    932    068 

513 

48 

13 

468    963    037 

506 

47 

14 

492    993    007 

499 

46 

15 

.67  515  .73  023  .26  977 

.94  492 

45 

16 

539    054    946 

485 

44 

17 

562    084    916 

479 

43 

18 

586    114    886 

472 

42 

19 

609    144    856 

465 

41 

20 

.67  633  .73  175  .26  825 

.94  458 

40 

21 

656    205    795 

451 

39 

22 

680    235    765 

445 

38 

23 

703    265    735 

438 

37 

24 

726    295    705 

431 

36 

25 

.67  750  .73  326  .26  674 

.94  424 

35 

26 

773    356    644 

417 

34 

27 

796    386    614 

410 

33 

28 

820    416    584 

404 

32 

29 

843    446    554 

397 

31 

30 

.67  866  .73  476  .26  524 

.94  390 

30 

31 

890    507    493 

383 

29 

32 

913    537   463 

376 

28 

33 

936    567    433 

369 

27 

34 

959   597   403 

362 

26 

35 

.67  982  .73  627  .26  373 

.94  355 

25 

36 

68  006    657    343 

349 

24 

37 

029    687    313 

342 

23 

38 

052    717    283 

335 

22 

39 

075    747    253 

328 

21 

40 

.68  098  .73  777  .26  223 

.94  321 

20 

41 

121    807    193 

314 

19 

42 

144    837    163 

307 

18 

43 

167   867    133 

300 

17 

44 

190    897    103 

293 

16 

45 

.68  213  .73  927  .26  073 

.94  286 

15 

46 

237    957    043 

279 

14 

47 

260    987    013 

273 

13 

48 

283  74  017  25  983 

266 

12 

49 

305   047   953 

259 

11 

50 

.68  328  .74  077  .25  923 

.94  252 

10 

51 

351    107   893 

245 

9 

52 

374    137   863 

238 

8 

53 

397    166    834 

231 

7 

54 

420    196    804 

224 

6 

55 

.68  443  .74  226  .25  774 

.94  217 

5 

56 

466    256    744 

210 

4 

57 

489    286    714 

203 

3 

58 

512    316    684 

196 

2 

59 

534    345    655 

189 

1 

60 

.68  557  .74  375  .25  625 

.94  182 

0 

9-10  9-10   0 

9-10 

1 

log  cos  log  cot  log  tan 

log  sin 

f 

63° 


61' 


38 

29° 

t 

log  sin  log  tan  log  cot  log  cos 

f 

9-10  9-10   0   9-10 

0 

.68  557  .74  375  .25  625  .94  182 

60 

1 

580    405    595    175 

59 

2 

603    435    565    168 

58 

3 

625    465    535    161 

57 

4 

648    494    506    154 

56 

5 

.68  671  .74  524  .25  476  .94  147 

55 

6 

694    554   446    140 

54 

7 

716   583   417    133 

53 

8 

739    613    387    126 

52 

9 

762    643    357    119 

51 

10 

.68  784  .74  673  .25  327  .94112 

50 

11 

807    702    298    105 

49 

12 

829    732    268    098 

48 

13 

852    762    238    090 

47 

14 

875    791    209   083 

46 

15 

.68  897  .74  821  .25  179  .94  076 

45 

16 

920    851    149    069 

44 

17 

942    880    120    062 

43 

18 

965    910   090    055 

42 

19 

987    939    061    048 

41 

20 

.69  010  .74  969  .25  031  .94  041 

40 

21 

032    998    002    034 

39 

22 

055  75  028  24  972    027 

38 

23 

077    058    942    020 

37 

24 

100   087    913    012 

36 

25 

.69122  .75  117  .24  883  .94  005 

35 

26 

144    146    854  93  998 

34 

27 

167    176    824    991 

33 

28 

189   205    795    984 

32 

29 

212   235    765   977 

31 

30 

.69  234  .75  264  .24  736  .93  970 

30 

31 

256    294    706    963 

29 

32 

279   323    677   955 

28 

33 

301    353    647    948 

27 

34 

323    382    618    941 

26 

35 

.69  345  .75  411  .24  589  .93  934 

25 

36 

368    441    559    927 

24 

37 

•  390   470    530    920 

23 

38 

412    500    500    912 

22 

39 

434    529    471    905 

21 

40 

.69  456  .75  558  .24  442  .93  898 

20 

41 

479    588    412    891 

19 

42 

501    617    383    884 

18 

43 

523   647   353   876 

17 

44 

545    676    324    869 

16 

45 

.69  567  .75  705  .24  295  .93  862 

15 

46 

589    735    265    855 

14 

47 

611    764    236    847 

13 

48 

633    793    207   840 

12 

49 

655    822    178    833 

11 

50 

.69  677  .75  852  .24  148  .93  826 

10 

51 

699    881    119    819 

9 

52 

721    910    090    811 

8 

53 

743    939    061    804 

7 

54 

765    969    031    797 

6 

55 

.69  787  .75  998  .24  002  .93  789 

5 

56 

809  76  027  23  973    782 

4 

57 

831    056   944    775 

3 

58 

853    086   914    768 

2 

59 

875    115    885    760 

1 

60 

.69  897  .76  144  .23  856  .93  753 
9-10   9-10    0   9-10 

0 

t 

log  cos  log  cot  log  tan  log  sin 

f 

30' 


f 

log  sin  log  tan  log  cot  log  cos 

t 

9-10  9-10   0   9-10 

0 

.69  897  .76  144  .23  856  .93  753 

60 

1 

919    173    827    746 

59 

2 

941    202    798    738 

58 

3 

963    231    769    731 

57 

4 

984    261    739    724 

56 

5 

.70  006  .76  290  .23  710  .93  717 

55 

6 

028    319    681    709 

54 

7 

050    348    652    702 

53 

8 

072    377    623    695 

52 

9 

093    406    594    687 

51 

10 

.70115  .76  435  .23  565  .93  680 

50 

11 

137    464    536    673 

49 

12 

159    493    507    665 

48 

13 

180    522    478    658 

47 

14 

202    551    449    650 

46 

15 

.70  224  .76  580  .23  420  .93  643 

45 

16 

245    609    391    636 

44 

17 

267    639    361    628 

43 

18 

288    668    332    621 

42 

19 

310   697   303   614 

41 

20 

.70  332  .76  725  .23  275  .93  606 

40 

21 

353    754    246    599 

39 

22 

375    783    217    591 

38 

23 

396    812    188    584 

37 

24 

418   841    159   577 

36 

25 

.70  439  .76  870  .23  130  .93  569 

35 

26 

461    899    101    562 

34 

27 

482    928    072    554 

33 

28 

504   957   043    547 

32 

29 

525   986   014   539 

31 

30 

.70  547  .77  015  .22  985  .93  532 

30 

31 

568    044    956    525 

29 

32 

590   073   927    517 

28 

33 

611    101    899    510 

27 

34 

633    130   870   502 

26 

35 

.70  654  .77  159  .22  841  .93  495 

25 

36 

675    188    812    487 

24 

37 

697    217    783    480 

23 

38 

718    246    754    472 

22 

39 

739    274    726    465 

21 

40 

.70  761  .77  303  .22  697  .93  457 

20 

41 

782    332    668    450 

19 

42 

803    361    639   442 

18 

43 

824    390   .  610    435 

17 

44 

846    418    582    427 

16 

45 

.70  867  .77  447  .22  553  .93  420 

15 

46 

888    476    524    412 

14 

47 

909    505    495    405 

13 

48 

931    533    467    397 

12 

49 

952    562    438    390 

11 

50 

.70  973  .77  591  .22  409  .93  382 

10 

51 

994    619    381    375 

9 

52 

71015    648    352    367 

8 

53 

036    677    323    360 

7 

54 

058    706    294    352 

6 

55 

.71  079  .77  734  .22  266  .93  344 

5 

56 

100    763    237    337 

4 

57 

121    791    209    329 

3 

58 

142    820    180    322 

2 

59 

163    849    151    314 

1 

60 

.71  184  .77  877  .22  123  .93  307 
9-10   9-10    0   9-10 

0 

t 

log  cos  log  cot  log  tan  log  sin 

t 

60^ 


59° 


31° 


t 

log  sin  log  tan  log  cot  log  cos 

t 

f 

9-10   9-10   0   9-10 

0 

.71  184  .77  877  .22  123  .93  307 

60 

1 

205    906    094    299 

59 

2 

226    935    065    291 

58 

3 

247    963    037    284 

57 

4 

268    992    008    276 

56 

5 

.71289  .78  020  .21980  .93  269 

65 

6 

310   049    951    261 

54 

7 

331   077   923    253 

53 

8 

352    106    894    246 

52 

9 

373    135    865    238 

51 

10 

.71  393  .78  163  .21  837  .93  230 

60 

11 

414    192    808    223 

49 

12 

435    220    780    215 

48 

13 

456    249    751    207 

47 

14 

477    277    723    200 

46 

16 

.71  498  .78  306  .21  694  .93  192 

46 

16 

519    334    666    184 

44 

17 

539   363    637    177 

43 

18 

560    391    609    169 

42 

19 

581    419    581    161 

41 

20 

.71602  .78  448  .21552  .93  154 

40 

21 

622    476    524    146 

39 

22 

643    505    495    138 

38 

23 

664   533   467    131 

37 

24 

685    562    438    123 

36 

25 

.71705  .78  590  .21410  .93  115 

36 

26 

726    618    382.   108 

34 

27 

747    647    353    100 

33 

28 

767    675    325    092 

32 

29 

788    704    296    084 

31 

30 

.71  809  .78  732  .21  268  .93  077 

30 

31 

829    760    240    069 

29 

32 

850    789    211    061 

28 

33 

870   817    183   053 

27 

34 

891    845    155    046 

26 

35 

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26 

36 

932    902    098    030 

24 

37 

952    930    070    022 

23 

38 

973    959    041    014 

22 

39 

994   987   013    007 

21 

40 

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20 

41 

034    043    957    991 

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42 

055    072   928   983 

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43 

075    100    900    976 

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44 

096    128    872    968 

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45 

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16 

46 

137    185    815    952 

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47 

157    213    787    944 

13 

48 

177   241    759   936 

12 

49 

198    269    731    929 

11 

50 

.72  218  .79  297  .20  703  .92  921 

10 

51 

238    326    674    913 

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52 

259    354    646    905 

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53 

279    382    618    897 

7 

54 

299    410    590    889 

6 

55 

.72  320  .79  438  .20  562  .92  881 

5 

56 

340    466    534    874 

4 

57 

360    495    505    866 

3 

58 

381    523    477    858 

2 

59 

401    551    449    850 

1 

60 

.72  421  .79  579  .20  421  .92  842 
9-10  9-10   0   9-10 

0 

f 

log  cos  log  cot  log  tan  log  sin 

t 

32° 

39 

1 

log  sin 

log  tan  log  cot 

log  cos 

f 

9-10 

9-10   0 

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0 

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60 

1 

441 

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542 

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10 

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783 

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21 

843 

168    832 

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863 

195    805 

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883 

223    777 

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13 

48 

699    527    473    173 

12 

49 

715    553    447    162 

11 

50 

.79  731  .90  578  .09  422  .89152 

10 

51 

746    604    396    142 

9 

52 

762    630    370    132 

8 

53 

778    656    344    122 

7 

54 

793    682    318    112 

6 

55 

.79  809  .90  708  .09  292  .89  101 

5 

56 

825    734    266   091 

4 

57 

840    759    241    081 

3 

58 

856   785    215    071 

2 

59 

872    811    189    060 

1 

60 

.79  887  .90  837  .09163  .89  050 

0 

9-10  9-10   0   9-10 

1 

log  cos  log  cot  log  tan  log  sin 

f 

52° 


51° 


39° 


f 

log  sin  log  tan  log  cot  log  cos 
9-10   9-10    0   9-10 

! 

0 

.79  887  .90  837  .09  163  .89  050 

60 

1 

903    863    137    040 

59 

2 

918    889    111    030 

58 

3 

934    914    086    020 

57 

4 

950    940   060   009 

56 

5 

.79  965  .90  966  .09  034  .88  999 

55 

6 

981    992    008   989 

54 

7 

996  91018  08  982    978 

53 

8 

80  012    043    957    968 

52 

9 

027    069    931    958 

51 

10 

.80  043  .91095  .08  905  .88  948 

50 

11 

058    121    879    937 

49 

12 

074    147    853    927 

48 

13 

089    172    828    917 

47 

14 

105    198    802    906 

46 

15 

.80  120  .91  224  .08  776  .88  896 

45 

16 

136    250    750    886 

44 

17 

151    276    724    875 

43 

18 

166    301    699    865 

42 

19 

182   327   673    855 

41 

20 

.80  197  .91  353  .08  647  .88  844 

40 

21 

213    379    621    834 

39 

22 

228    404    596    824 

38 

23 

244    430    570    813 

37 

24 

259    456    544    803 

36 

25 

.80  274  .91482  .08  518  .88  793 

35 

26 

290    507    493    782 

34 

27 

305    533    467    772 

33 

28 

320    559    441    761 

32 

29 

336   585    415    751 

31 

30 

.80  351  .91610  .08  390  .88  741 

30 

31 

366    636    364    730 

29 

32 

382    662    338    720 

28 

33 

397    688    312    709 

27 

34 

412    713    287    699 

26 

35 

.80  428  .91  739  .08  261  .88  688 

25 

36 

443    765    235    678 

24 

37 

458    791    209    668 

23 

38 

473    816    184    657 

22 

39 

489    842    158    647 

21 

40 

.80  504  .91  868  .08  132  .88  636 

20 

41 

519    893    107    626 

19 

42 

534    919    081    615 

18 

43 

550    945    055    605 

17 

44 

565    971    029    594 

16 

45 

.80  580  .91996  .08  004  .88  584 

15 

46 

595  92  022  07  978    573 

14 

47 

610    048    952    563 

13 

48 

625    073    927    552 

12 

49 

641    099    901    542 

11 

50 

.80  656  .92  125  .07  875  .88  531 

10 

51 

671    150    850    521 

9 

52 

686    176    824    510 

8 

53 

701    202    798    499 

7 

54 

716   227    773   489 

6 

55 

.80  731  .92  253  .07  747  .88  478 

5 

56 

746    279    721    468 

4 

57 

762    304    696   457 

3 

58 

777    330    670    447 

2 

59 

792    356    644    436 

1 

60 

.80  807  .92  381  .07  619  .88  425 
9-10   9-10   0   9-10 

0 

1 

log  cos  log  cot  log  tan  log  sin 

t 

40° 

43 

t 

log  sin  log  tan  log  cot  log  cos 

1 

**9-10   9-10   0   9-10 

0 

.80  807  .92  381  .07  619  .88  425 

60 

1 

822    407    593    415 

59 

2 

837    433    567    404 

58 

3 

852    458    542    394 

57 

4 

867    484    516    383 

56 

5 

.80  882  .92  510  .07  490  .88  372 

55 

6 

897    535    465    362 

54 

7 

912    561    439    351 

53 

8 

927    587    413    340 

52 

9 

942    612    388   330 

51 

10 

.80  957  .92  638  .07  362  .88  319 

50 

11 

972    663    337    308 

49 

12 

987    689    311    298 

48 

13 

81002    715    285    287 

47 

14 

017    740    260    276 

46 

15 

.81  032  .92  766  .07  234  .88  266 

45 

16 

047    792    208    255 

44 

17 

061    817    183    244 

43 

18 

076    843    157    234 

42 

19 

091    868    132    223 

41 

20 

.81  106  .92  894  .07  106  .88  212 

40 

21 

121    920    080    201 

39 

22 

136   945    055    191 

38 

23 

151    971    029    180 

37 

24 

166    996    004    169 

36 

25 

.81  180  .93  022  .06  978  .88  158 

35 

26 

195    048    952    148 

34 

27 

210    073    927    137 

33 

28 

225    099    901    126 

32 

29 

240    124    876    115 

31 

30 

.81  254  .93  150  .06  850  .88  105 

30 

31 

269    175    825    094 

29 

32 

284    201    799   083 

28 

33 

299    227    773    072 

27 

34 

314    252    748    061 

26 

35 

.81328  .93  278  .06  722  .88  051 

25 

36 

343    303    697    040 

24 

37 

358    329    671    029 

23 

38 

372    354    646   018 

22 

39 

387   380   620   007 

21 

40 

.81402  .93  406  .06  594  .87  996 

20 

41 

417    431    569    985 

19 

42 

431    457    543    975 

18 

43 

446    482    518    964 

17 

44 

461    508    492    953 

16 

45 

.81  475  .93  533  .06  467  .87  942 

15 

46 

490    559    441    931 

14 

47 

505    584    416    920 

13 

48 

519    610    390    909 

12 

49 

534    636    364    898 

11 

50 

.81  549  .93  661  .06  339  .87  887 

10 

51 

563    687    313    877 

9 

52 

578    712    288    866 

8 

53 

592    738    262    855 

7 

54 

607    763    237    844 

6 

55 

.81622  .93  789  .06  211  .87  833 

5 

56 

636    814    186    822 

4 

57 

651    840    160    811 

3 

58 

665    865    135    800 

2 

59 

680    891    109    789 

1 

60 

.81  694  .93  916  .06  084  .87  778 

0 

9-10  9-10   0   9-10 

t 

log  cos  log  cot  log  tan  log  sin 

f 

50< 


49< 


44 


41^ 


42° 


o_4.o 
2418 

f 

log  sin  log  tan  log  cot  log  cos 

f 

f 

log  sin  log  tan  log  cot  log  cos 

f 

.2419 

9-10  9-10   0   9-10 

9-10   9-10   0   9-10 

0580 

0 

.81  694  .93  916  .06  084  .87  778 

60 

0 

.82  551  .95  444  .04  556  .87107 

60 

)9  834 

1 

709    942    058    767 

59 

1 

565    469    531    096 

59 

50-88° 

2 

723    967    033    756 

58 

2 

579    495    505    085 

58 

o_8o 
940*^ 

3 

738   993   007    745 

57 

3 

593    520   480    073 

57 

4 

752  94  018  05  982    734 

56 

4 

607    545    455    062 

56 

9419 

5 

.81  767  .94  044  .05  956  .87  723 

55 

5 

.82  621  .95  571  .04  429  .87  050 

55 

JO  029 

6 

781    069    931    712 

54 

6 

635    596    404    039 

54 

)9  462 

7 

796   095    905    701 

53 

7 

649    622    378    028 

53 

l°-84° 

8 

810    120    880    690 

52 

8 

663    647    353    016 

52 

9 

825    146    854    679 

51 

9 

677    672    328    005 

51 

°-12° 

10 

.81839  .94  171  .05  829  .87  668 

50 

10 

.82  691  .95  698  .04  302  .86  993 

50 

1.9  433 
19  971 
33  664 

11 

854    197    803    657 

49 

11 

705    723    277    982 

49 

12 

868    222    778    646 

48 

12 

719    748    252    970 

48 

)8  872 

13 

882    248    752    635 

47 

13 

733    774    226    959 

47 

70-80'^ 

14 

897    273    727    624 

46 

14 

747    799    201    947 

46 

15 

.81911  .94  299  .05  701  .87  613 

45 

15 

.82  761  .95  825  .04  175  .§6  936 

45 

13°-1( 

16 

926    324    676    601 

44 

16 

775    850    150    924 

44 

.35  201 
.36  33. 
.51  46< 
.98  06< 

17 

940    350    650    590 

43 

17 

788   875    125    913 

43 

18 

955    375    625    579 

42 

18 

802    901    099    902 

42 

19 

969    401    599    568 

41 

19 

816    926    074    890 

41 

j^o-'y 

20 

.81983  .94  426  .05  574  .87  557 

40 

20 

.82  830  .95  952  .04  048  .86  879 

40 

21 

998    452    548    546 

39 

21 

844    977    023    867 

39 

0-20° 

22 

82  012    477    523    535 

38 

22 

858  96  002  03  998    855 

38 

5  594 

23 

026    503    497    524 

37 

23 

872    028    972    844 

37 

J  534 

24 

041    528    472    513 

36 

24 

885    053    947    832 

36 

582 
015 

25 

.82  055  .94  554  .05  446  .87  501 

35 

25 

.82  899  .96  078  .03  922  .86  821 

35 

0-720 

26 

069    579   421    490 

34 

26 

913    104    896    809 

34 

27 

084    604    396    479 

33 

27 

927    129    871    798 

33 

210-24° 

28 

098    630    370    468 

31 

28 

941    155    845    786 

32 

.55  433 

29 

112    655    345    457 

31 

29 

955    180   820   775 

31 

.58  418 
.33  133 
.95  728 
65°-68'^ 

30 

.82  126  .94  681  .05  319  .87  446 

30 

30 

.82  968  .96  205  .03  795  .86  763 

30 

31 

141    706    294    434 

29 

31 

982    231    769    752 

29 

32 

155    732    268    423 

28 

32 

996    256    744    740 

28 

33 

169    757    243    412 

27 

33 

83  010   281    719    728 

27 

25°-28= 

34 

184    783    217    401 

26 

34 

023    307    693    717 

26 

.62  595 
.66  867 
.25  625 
.94  182 

35 

.82  198  .94  808  .05  192  .87  390 

25 

35 

.83  037  .96  332  .03  668  .86  705 

25 

36 

212    834    166    378 

24 

36 

051    357    643    694 

24 

37 

226    859    141    367 

23 

37 

065    383    617    682 

23 

61o-64^ 

38 

240    884    116   356 

22 

38 

078    408    592    670 

22 

39 

255    910    090    345 

21 

39 

092    433    567    659 

21 

9°-32° 

40 

.82  269  .94  935  .05  065  .87  334 

20 

40 

.83  106  .96  459  .03  541  .86  647 

20 

38  557 

41 

283    961    039    322 

19 

41 

120    484    516    635 

19 

'4  375 

18  748 
32  359 

42 

297    986   014    311 

18 

42 

133    510   490    624 

18 

43 

311  95  012  04  988    300 

17 

43 

147    535    465    612 

17 

7°-60° 

44 

326    037    963    288 

16 

44 

161    560    440    600 

16 

°-36° 

45 

.82  340  .95  062  .04  938  .87  277 

16 

45 

.83  174  .96  586  .03  414  .86  589 

15 

5  611 

46 

354    088    912    266 

14 

46 

188    611    389    577 

14 

252 

47 

368    113   887   255 

13 

47 

202    636    364    565 

13 

5  289 

48 

382    139    861    243 

12 

48 

215    662    338    554 

12 

)235 
°-56° 

49 

396    164    836    232 

11 

49 

229    687    313    542 

11 

50 

.82  410  .95  190  .04  810  .87  221 

10 

50 

.83  242  .96  712  .03  288  .86  530 

10 

51 

424    215    785    209 

9 

51 

256    738    262    518 

9 

370-40° 

52 

439    240    760    198 

8 

52 

270   763   237   507 

8 

.77  946 

53 

453    266    734    187 

7 

53 

283    788    212    495 

7 

.87  711 
.06  084 

.87  778 

54 

467    291    709    175 

6 

54 

297    814    186    483 

6 

55 

.82  481  .95  317  .04  683  .87164 

5 

55 

.83  310  .96  839  .03  161  .86  472 

5 

4qo  ftP^ 

56 

495    342    658    153 

4 

56 

324    864    136   460 

4 

57 

509    368    632    141 

3 

57 

338    890    110    448 

3 

41°-44o 

58 

523    393    607    130 

2 

58 

351    915    085    436 

2 

.81  694 
.93  916 
.00  000 

59 

537    418    582    119 

1 

59 

365    940   060   425 

1 

60 

.82  551  .95  444  .04  556  .87107 

0 

60 

.83  378  .96  966  .03  034  .86  413 

0 

.84  949 

9-10  9-10   0   9-10 

9-10  9-10   0   9-10 

45°-48° 

t 

log  cos  log  cot  log  tan  log  sin 

f 

F 

log  cos  log  cot  log  tan  log  sin 

f 

48< 


47< 


1 

log  sin 

log  tan 

log  cot  log  COS 

f 

9-10 

9-10 

0 

9-10 

0 

.83  378 

.96  966 

.03  034 

.86  413 

60 

1 

392 

991 

009 

401 

59 

2 

405 

97  016 

02  984 

389 

58 

3 

419 

042 

958 

377 

57 

4 

432 

067 

933 

366 

56 

5 

.83  446 

.97  092 

.02  908 

.86  354 

55 

6 

459 

118 

882 

342 

54 

7 

473 

143 

857 

330 

53 

8 

486 

168 

832 

318 

52 

9 

500 

193 

807 

306 

51 

10 

.83  513 

.97  219 

.02  781 

.86  295 

50 

11 

527 

244 

756 

283 

49 

12 

540 

269 

731 

271 

48 

13 

554 

295 

705 

259 

47 

14 

567 

320 

680 

247 

46 

15 

.83  581 

.97  345 

.02  655 

.86  235 

45 

16 

594 

371 

629 

223 

44 

17 

608 

396 

604 

211 

43 

18 

621 

421 

579 

200 

42 

19 

634 

447 

553 

188 

41 

20 

.83  648 

.97  472 

.02  528 

.86  176 

40 

21 

661 

497 

503 

164 

39 

22 

674 

523 

477 

152 

38 

23 

688 

548 

452 

140 

37 

24 

701 

573 

427 

128 

36 

25 

.83  715 

.97  598 

.02  402 

.86116 

35 

26 

728 

624 

376 

104 

34 

27 

741 

649 

351 

092 

33 

28 

755 

674 

326 

080 

32 

29 

768 

700 

300 

068 

31 

30 

.83  781 

.97  725 

.02  275 

.86  056 

30 

31 

795 

750 

250 

044 

29 

32 

808 

776 

224 

032 

28 

33 

821 

801 

199 

020 

27 

34 

834 

826 

174 

008 

26 

35 

.83  848 

.97  851 

.02  149 

.85  996 

25 

36 

861 

877 

123 

984 

24 

37 

874 

902 

098 

972 

23 

38 

887 

927 

073 

960 

22 

39 

901 

953 

047 

948 

21 

40 

.83  914 

.97  978 

.02  022 

.85  936 

20 

41 

927 

98  003 

01997 

924 

19 

42 

940 

029 

971 

912 

18 

43 

954 

054 

946 

900 

17 

44 

967 

079 

921 

888 

16 

45 

.83  980 

.98  104 

.01  896 

.85  876 

15 

46 

993 

130 

870 

864 

14 

47 

84  006 

155 

845 

851 

13 

48 

020 

180 

820 

839 

12 

49 

033 

206 

794 

827 

11 

50 

.84  046 

.98  231 

.01  769 

.85  815 

10 

51 

059 

256 

744 

803 

9 

52 

072 

281 

719 

791 

8 

53 

085 

307 

693 

779 

7 

54 

098 

332 

668 

766 

6 

55 

.84  112 

.98  357 

.01  643 

.85  754 

5 

56 

125 

383 

617 

742 

4 

57 

138 

408 

592 

730 

3 

58 

151 

433 

567 

718 

2 

59 

164 

458 

542 

706 

1 

60 

.84  177 

.98  484 

.01  516 

.85  693 

0 

9-10 

9-10 

0 

9-10 

r 

log  cos 

log  cot 

log  tan 

log  sin 

1 

440 

45 

1 

log  sin  log  tan  log  cot  log  cos 

f 

9-10   9-10    0   9-10 

0 

.84  177  .98  484  .01516  .85  693 

60 

1 

190    509   491    681 

59 

2 

203    534    466    669 

58 

3 

216    560   440   657 

57 

4 

229    585    415    645 

56 

5 

.84  242  .98  610  .01  390  .85  632 

55 

6 

255    635    365    620 

54 

7 

269    661    339   608 

53 

8 

282    686    314    596 

52 

9 

295    711    289    583 

51 

10 

.84  308  .98  737  .01  263  .85  571 

50 

11 

321    762    238    559 

49 

12 

334    787    213    547 

48 

13 

347    812    188    534 

47 

14 

360    838    162    522 

46 

15 

.84  373  .98  863  .01137  .85  510 

45 

16 

385    888    112    497 

44 

17 

398   913   087   485 

43 

18 

411    939    061    473 

42 

19 

424    964    036   460 

41 

20 

.84  437  .98  989  .01011  .85  448 

40 

21 

450  99  015  00  985    436 

39 

22 

463    040    960   423 

38 

23 

476    065    935    411 

37 

24 

489    090    910   399 

36 

25 

.84  502  .99  116  .00  884  .85  386 

35 

26 

515    141    859   374 

34 

27 

528    166    834   361 

33 

28 

540    191    809   349 

32 

29 

553    217   783   337 

31 

30 

.84  566  .99  242  .00  758  .85  324 

30 

31 

579    267    733    312 

29 

32 

592    293    707    299 

28 

33 

605    318    682    287 

27 

34 

618   343   657   274 

26 

35 

.84  630  .99  368  .00  632  .85  262 

25 

36 

643    394    606    250 

24 

37 

656   419    581    237 

23 

38 

669   444    556    225 

22 

39 

682    469    531    212 

21 

40 

.84  694  .99  495  .00  505  .85  200 

20 

41 

707    520   480    187 

19 

42 

720    545    455    175 

18 

43 

733    570   430    162 

17 

44 

745    596    404    150 

16 

45 

.84  758  .99  621  .00  379  .85  137 

15 

46 

771    646    354    125 

14 

47 

784    672    328    112 

13 

48 

796   697    303    100 

12 

49 

809    722    278    087 

11 

50 

.84  822  .99  747  .00  253  .85  074 

10 

51 

835    773    227    062 

9 

52 

847    798    202    049 

8 

53 

860   823    177   037 

7 

54 

873    848    152    024- 

6 

55 

.84  885  .99  874  .00126  .85  012 

5 

56 

898    899    101  84  999 

4 

57 

911    924    076    986 

3 

58 

923    949    051    974 

2 

59 

936    975    025    961 

1 

60 

F 

.84  949  .00  000  .00  000  .84  949 

9-10    0    0   9-10 

log  cos  log  cot  log  tan  log  sin 

0 
r 

46^ 


45° 


46 


TABLE  IV 

THE  LOGARITHMS 

OF  THE 

TEIGONOMETRIC 

FUNCTIONS 

OF  ANGLES 

From  0'  to  3' 

and  89° 

57'  to  90°,  for  every  second 

From  3'  to  2° 

and  88° 

to  89°  57',  for  every 

'  ten  seconds 

log  cos  A 

=  0.00  000,  when  0'  <  ^  <  16' 

log  sin  A 

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31 
32 
33 
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5.38  454 
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35 

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37 
38 
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24 
23 
22 
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10 

11 
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5.68  557 
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80  285 

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47 
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40 

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42 
43 
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31904 
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69  418 
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89  240 
509 
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19 
18 
17 
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15 

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5.86  167 
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14 
13 
12 
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20 

21 
22 
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5.98  660 

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02  800 

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06  579 

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50 

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4.08  351 
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When  the 

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than  3'  or  greater  than  89°  57 

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when  the  given  logarithmic  func- 

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suit  the  page  opposite. 

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20 

50 

243 

247 

996 

10 

50 

333 

339 

994 

10 

49  0 

.15  391 

.15  395 

.99  996 

0  11 

59  0 

.23  456 

.23  462 

.99  994 

0  1 

10 

538 

543 

996 

50 

10 

578 

585 

994 

50 

20 

685 

690 

996 

40 

20 

700 

707 

994 

40 

30 

832 

836 

995 

30 

30 

822 

829 

993 

30 

40 

978 

982 

995 

20 

40 

944 

950 

993 

20 

50 

16123 

16128 

995 

10 

50 

24  065 

24  071 

993 

10 

50  0 

.16  268 
8-10 

.16  273 
8-10 

.99  995 

0  10 

60  0 

.24  186 

.24  192 

.99  993 

0  0 

9-10 

8-10 

8-10 

9-10 

f  n 

log  cos 

log  cot 

log  sin 

11    1 

1    II 

log  COS 

log  cot 

log  sin 

II    1 

89° 


50 


1   n 

log  sin 

log  tan 

log  COS 

n    1 

f  ff 

log  sin 

log  tan 

log  cos 

ff  f 

8-10 

.24  186 

8-10 

.24  192 

9-10 

.99  993 

8-10 

.30  879 

8-10 

.30  888 

9-10 

.99  991 

0  0 

0   60 

10  0 

0  50 

10 

306 

313 

993 

50 

]0 

983 

992 

991 

50 

20 

426 

433 

993 

40 

20 

31086 

31095 

991 

40 

30 

546 

553 

993 

30 

30 

188 

198 

991 

30 

40 

665 

672 

993 

20 

40 

291 

300 

991 

20 

50 

785 

791 

993 

10 

50 

393 

403 

991 

10 

1  0 

.24  903 

.24  910 

.99  993 

0  59 

11  0 

.31  495 

.31  505 

.99  991 

0  49 

10 

25  022 

25  029 

993 

50 

10 

597 

606 

991 

50 

20 

140 

147 

993 

40 

20 

699 

708 

991 

40 

30 

258 

265 

993 

30 

30 

800 

809 

991 

30 

40 

375 

382 

993 

20 

40 

901 

911 

991 

20 

50 

493 

500 

993 

10 

50 

32  002 

32  012 

991 

10 

2  0 

.25  609 

.25  616 

.99  993 

0  58 

12  0 

.32  103 

.32  112 

.99  990 

0  48 

10 

726 

733 

993 

50 

10 

203 

213 

990 

50 

20 

842 

849 

993 

40 

20 

303 

313 

990 

40 

30 

958 

965 

993 

30 

30 

403 

413 

990 

30 

0'-20' 

40 

26  074 

26  081 

993 

20 

40 

503 

513 

990 

20 

50 

189 

196 

993 

10 

50 

602 

612 

990 

10 

U.UO  J  J 

6.68  55 

3  0 

.26  304 

.26  312 

.99  993 

0  57 

13  0 

.32  702 

.32  711 

.99  990 

0  47 

1.99  99 

10 

419 

426 

993 

50 

10 

801 

810 

990 

50 

89°  40' 

20 

533 

541 

993 

40 

20 

899 

909 

990 

40 

-90° 

30 

648 

655 

993 

30 

30 

998 

33  008 

990 

30 

40 

761 

769 

993 

20 

40 

33  096 

106 

990 

20 

50 

875 

882 

993 

10 

50 

195 

205 

990 

10 

20^-60 

4  0 

.26  988 

.26  996 

.99  992 

0  66 

14  0 

.33  292 

.33  302 

.99  990 

0  46 

3.76  4: 
3.76  4: 

10 

27  101- 

27109 

992 

50 

10 

390 

400 

990 

50 

20 

214 

221 

992 

40 

20 

488 

498 

990 

40 

T.99  9S 

30 

326 

334 

992 

30 

30 

585 

595 

990 

30 

89°- 

40 

438 

446 

992 

20 

40 

682 

692 

990 

20 

89°  4^ 

50 

550 

558 

992 

10 

50 

779 

789 

990 

10 

1°-1°  40' 

5  0 

.27  661 

.27  669 

.99  992 

0  55 

15  0 

.33  875 

.33  886 

.99  990 

0  45 

2.24  18 

10 

773 

780 

992 

50 

10 

972 

982 

990 

50 

2.24  19 

20 

883 

891 

992 

40 

20 

34  068 

34  078 

990 

40 

T.99  98 

30 

994 

28  002 

992 

30 

30 

164 

174 

990 

30 

88°  20' 

40 

28104 

112 

992 

20 

40 

260 

270 

989 

20 

-89° 

50 

215 

223 

992 

10 

50 

355 

366 

989 

10 

6  0 

.28  324 

.28  332 

.99  992 

0  54 

16  0 

.34  450 

.34  461 

.99  989 

0  44 

10 

434 

442 

992 

50 

10 

546 

556 

989 

50 

20 

543 

551 

992 

40 

20 

640 

651 

989 

40 

30 

652 

660 

992 

30 

30 

735 

746 

989 

30 

40 

761 

769 

992 

20 

40 

830 

840 

989 

20 

50 

869 

877 

992 

10 

50 

924 

935 

989 

10 

7  0 

.28  977 

.28  986 

.99  992 

0  53 

17  0 

.35  018 

.35  029 

.99  989 

0  43 

10 

29  085 

29  094 

992 

50 

10 

112 

123 

989 

50 

20 

193 

201 

992 

40 

20 

206 

217 

989 

40 

30 

300 

309 

992 

30 

30 

299 

310 

989 

30 

40 

407 

416 

992 

20 

40 

392 

403 

989 

20 

50 

514 

523 

992 

10 

50 

485 

497 

989 

10 

8  0 

.29  621 

.29  629 

.99  992 

0  52 

18  0 

.35  578 

.35  590 

.99  989 

0  42 

10 

727 

736 

991 

50 

10 

671 

682 

989 

50 

20 

833 

842 

991 

40 

20 

764 

775 

989 

40 

iHB^ 

30 

939 

947 

991 

30 

30 

856 

867 

989 

30 

^^K 

40 

30044 

30  053 

991 

20 

40 

948 

959 

989 

20 

B. 

50 

150 

158 

991 

10 

50 

36040 

36  051 

989 

10 

mttm'' 

9  0 

.30  255 

.30  263 

.99  991 

0  51 

19  0 

.36  131 

.36  143 

.99  989 

0  41 

10 

359 

368 

991 

50 

10 

223 

235 

988 

50 

20 

464 

473 

991 

40 

20 

314 

326 

988 

40 

30 

568 

577 

991 

30 

30 

405 

417 

988 

30 

40 

672 

681 

991 

20 

40 

496 

508 

988 

20 

50 

776 

785 

991 

10 

50 

587 

599 

988 

10 

10  0 

.30  879 

.30  888 

.99  991 

0  50 

20  0 

.36  678 

.36  689 

.99  988 
9-10 

0  40 

8-10 

8-10 

9-10 

8-10 

8-10 

f  ff 

log  cos 

log  cot 

log  sin 

rr  / 

r  ff 

log  cos 

log  cot 

log  sin 

ff  f 

88' 


1« 


51 


1    If 

log  sin 

log  tan 

log  cos 

II    1 

1    II 

log  sin 

log  tan 

log  cos 

n    1 

8-10 

.36  678 

8-10 

.36  689 

9-10 

.99  988 

8-10 

.41  792 

8-10 

.41  807 

9-10 

.99  985 

20  0 

0   40 

80  0 

0   30 

10 

768 

780 

988 

50 

10 

872 

887 

985 

50 

20 

858 

870 

988 

40 

20 

952 

967 

985 

40 

30 

948 

960 

988 

30 

30 

42  032 

42  048 

985 

30 

40 

37  038 

37  050 

988 

20 

40 

112 

127 

985 

20 

50 

128 

140 

988 

10 

50 

192 

207 

985 

10 

21  0 

.37  217 

.37  229 

.99  988 

0  39 

31  0 

.42  272 

.42  287 

.99  985 

0  29 

10 

306 

318 

988 

50 

10 

351 

366 

985 

50 

20 

395 

408 

988 

40 

20 

430 

446 

985 

40 

30 

484 

497 

988 

30 

30 

510 

525 

985 

30 

40 

573 

585 

988 

20 

40 

589 

604 

985 

20 

50 

662 

674 

988 

10 

50 

667 

683 

985 

10 

22  0 

.37  750 

.37  762 

.99  988 

0  38 

32  0 

.42  746 

.42  762 

.99  984 

0  28 

10 

838 

850 

988 

50 

10 

825 

840 

984 

50 

20 

926 

938 

988 

40 

20 

903 

919 

984 

40 

30 

38  014 

38  026 

987 

30 

30 

982 

997 

984 

30 

40 

101 

114 

987 

20 

40 

43  060 

43  075 

984 

20 

50 

189 

202 

987 

10 

50 

138 

154 

984 

10 

23  0 

.38  276 

.38  289 

.99  987 

0  37 

33  0 

-.43  216 

.43  232 

.99  984 

0  27 

10 

363 

376 

987 

50 

10 

293 

309 

984 

50 

20 

450 

463 

987 

40 

20 

371 

.   387 

984 

40 

30 

537 

550 

987 

30 

30 

448 

464 

984 

30 

40 

624 

636 

987 

20 

40 

526 

542 

984 

20 

50 

710 

723 

987 

10 

50 

603 

619 

984 

10 

24  0 

.38  796 

.38  809 

.99  987 

0  36 

34  0 

.43  680 

.43  696 

.99  984 

0  26 

10 

882 

895 

987 

50 

10 

757 

773 

984 

50 

20 

968 

981 

987 

40 

20 

834 

850 

984 

40 

30 

39  054 

39  067 

987 

30 

30 

910 

927 

984 

30 

40 

139 

153 

987 

20 

40 

987 

44  003 

984 

20 

50 

225 

238 

987 

10 

50 

44  063 

080 

983 

10 

25  0 

.39  310 

.39  323 

.99  987 

0  35 

35  0 

.44  139 

.44  156 

.99  983 

0  25 

10 

395 

408 

987 

50 

10 

216 

232 

983 

50 

20 

480 

493 

987 

40 

20 

292 

308 

983 

40 

30 

565 

578 

987 

30 

30 

367 

384 

983 

30 

40 

649 

663 

987 

20 

40 

443 

460 

983 

20 

50 

734 

747 

986 

10 

50 

519 

536 

983 

10 

26  0 

.39  818 

.39  832 

.99  986 

0  34 

36  0 

.44  594 

.44  611 

.99  983 

0  24 

10 

902 

916 

986 

50 

10 

669 

686 

983 

50 

20 

986 

40  000 

986 

40 

20 

745 

762 

983 

40 

30 

40  070 

083 

986 

30 

30 

820 

837 

983 

30 

40 

153 

167 

986 

20 

40 

895 

912 

983 

20 

50 

237 

250 

986 

10 

50 

969 

987 

983 

10 

27  0 

.40  320 

.40  334 

.99  986 

0  33 

37  0 

.45  044 

.45  061 

.99  983 

0  23 

10 

403 

417 

986 

50 

10 

119 

136 

983 

50 

20 

486 

500 

986 

40 

20 

193 

210 

983 

40 

30 

569 

583 

986 

30 

30 

267 

285 

983 

30 

40 

651 

665 

986 

20 

40 

341 

359 

982 

20 

50 

734 

748 

986 

10 

50 

415 

433 

982 

10 

28  0 

.40  816 

.40  830 

.99  986 

0  32 

38  0 

.45  489 

.45  507 

.99  982 

0  22 

10 

898 

913 

986 

50 

10 

563 

581 

982 

50 

20 

980 

995 

986 

40 

20 

637 

655 

982 

40 

30 

41062 

41077 

986 

30 

30 

710 

728 

982 

30  MlHl 

40 

144 

158 

986 

20 

40 

784 

802 

982 

20  ^^^H 

50 

225 

240 

985 

10 

50 

857 

875 
.45  948 

982 
.99982 

10  ^HH 

29  0 

.41  307 

.41  321 

.99  985 

0  31 

39  0 

.45  930 

0  21 

10 

388 

403 

985 

50 

10 

46  003 

46  021 

982 

50 

20 

469 

484 

985 

40 

20 

076 

094 

982 

40 

30 

550 

565 

985 

30 

30 

149 

167 

982 

30 

40 

631 

646 

985 

20 

40 

222 

240 

982 

20 

,  50 

711 

726 

985 

10 

50 

294 

312 

982 

10 

30  0 

.41  792 

.41  807 

.99985 

0  30 

40  0 

.46  366 

.46  385 

.99982 
9-10 

0  20 

8-10 

8-10 

9-10 

8-10 

8-10 

1    11 

log  cos 

log  cot 

log  sin 

11    1 

1    It 

log  cos 

log  cot 

log  sin 

II    1 

88^ 


52 

1 

o 

1    n 

log  sin 

log  tan 

log  cos 

1!     t 

1    II 

log  sin 

log  tan 

log  COS 

It    1 

8-10 

8-10 

9-10 

8-10 

8-10 

9-10 

40  0 

.46  366 

.46  385 

.99  982 

0   20 

50  0 

.50  504 

.50  527 

.99  978 

0   10 

10 

439 

457 

982 

50 

10 

570 

593 

978 

50 

20 

511 

529 

982 

40 

20 

636 

658 

978 

40 

30 

583 

602 

981 

30 

30 

701 

724 

978 

30 

40 

655 

674 

981 

20 

40 

767 

789 

977 

20 

50 

727 

745 

981 

10 

50 

832 

S55 

977 

10 

41  0 

.46  799 

.46  817 

.99  981 

0  19 

51  0 

.50  897 

.50  920 

.99  977 

0  9 

10 

870 

889 

981 

50 

10 

963 

985 

977 

50 

20 

942 

960 

981 

40 

20 

51028 

51050 

977 

40 

30 

47  013 

47  032 

981 

30 

30 

092 

115 

977 

30 

40 

084 

103 

981 

20 

40 

157 

180 

977 

20 

50 

155 

174 

981 

10 

50 

222 

245 

977 

10 

42  0 

.47  226 

.47  245 

.99  981 

0  18 

52  0 

.51  287 

.51  310 

.99  977 

0  8 

10 

297 

316 

981 

50 

10 

351 

374 

977 

50 

20 

368 

387 

981 

40 

20 

416 

439 

977 

40 

30 

439 

458 

981 

30 

30 

480 

503 

977 

30 

0'-20' 

40 

509 

528 

981 

20 

40 

544 

568 

977 

20 

5.68  55 

50 

580 

599 

981 

10 

50 

609 

632 

977 

10 

6.68  55 

43  0 

.47  650 

.47  669 

.99  981 

0  17 

53  0 

.51673 

.51  696 

.99  977 

0  7 

1.99  99 

'   10 

720 

740 

980 

50 

10 

737 

760 

976 

50 

89°  40' 

20 

790 

810 

980 

40 

20 

801 

824 

976 

40 

-90° 

30 

860 

880 

980 

30 

30 

864 

888 

976 

30 

40 

930 

950 

980 

20 

40 

928 

952 

976 

20 

20'-60 

50 

48  000 

48  020 

980 

10 

50 

992 

52  015 

976 

10 

3.76  4: 

44  0 

.48  069 

.48  089 

.99  980 

0  16 

54  0 

.52  055 

.52  079 

.99  976 

0  6 

3.76  4; 

10 

139 

159 

980 

50 

10 

119 

143 

976 

50 

T.99  9S 

20 

208 

228 

980 

40 

20 

182 

206 

976 

40 

89°- 

30 

278 

298 

980 

30 

30 

245 

269 

976 

30 

89°  A'' 

40 

347 

367 

980 

20 

40 

308 

332 

976 

20 

50 

416 

436 

980 

10 

50 

371 

396 

976 

10 

1°-1°  40 

2.24  18 
2.24  19 
1.99  98 

45  0 

.48  485 

.48  505 

.99  980 

0  15 

55  0 

.52  434 

.52  459 

.99  976 

0  5 

10 

554 

574 

980 

50 

10 

497 

522 

976 

50 

20 

622 

643 

980 

40 

20 

560 

584 

976 

40 

30 

691 

711 

980 

30 

30 

623 

647 

975 

30 

88°  20' 

40 

760 

780 

979 

20 

40 

685 

710 

975 

20 

-89° 

50 

828 

849 

979 

10 

50 

748 

772 

975 

10 

46  0 

.48  896 

.48  917 

.99  979 

0  14 

56  0 

.52  810 

.52  835 

.99  975 

0  4 

1°  40-2° 

10 

965 

985 

979 

50 

10 

872 

897 

975 

50 

2.46  36 

20 

49  033 

49  053 

979 

40 

20 

935 

960 

975 

40 

2.46  38 

30 

101 

121 

979 

30 

30 

997 

53  022 

975 

30 

T.99  97 

40 

169 

189 

979 

20 

40 

53  059 

084 

975 

20 

88°- 

50 

236 

257 

979 

10 

50 

121 

146 

975 

10 

88°  20' 

47  0 

.49  304 

.49  325 

.99  979 

0  13 

57  0 

.53  183 

.53  208 

.99  975 

0  3 

10 

372 

393 

979 

50 

10 

245 

270 

975 

50 

20 

439 

460 

979 

40 

20 

306 

332 

975 

40 

30 

506 

528 

979 

30 

30 

368 

393 

975 

30 

40 

574 

595 

979 

20 

40 

429 

455 

975 

20 

50 

641 

662 

979 

10 

50 

491 

516 

974 

10 

48  0 

.49  708 

.49  729 

.99  979 

0  12 

58  0 

.53  552 

.53  578 

.99  974 

0  2 

10 

775 

796 

979 

50 

10 

614 

639 

974 

50 

^^^^^^^ 

1   20 

842 

863 

978 

40 

20 

675 

700 

974 

40 

HH^^^^I 

{     30 

908 

930 

978 

30 

30 

736 

762 

974 

30 

^^^^^^1 

1  40 

975 

997 

978 

20 

40 

797 

823 

974 

20 

^H^^B 

1  50 

50  042 

50  063 

978 

10 

50 

858 

884 

974 

10 

49  0 

.50  108 

.50  130 

.99  978 

0  11 

59  0 

.53  919 

.53  945 

.99  974 

0  1 

10 

174 

196 

978 

50 

10 

979 

54  005 

974 

50 

20 

241 

263 

978 

40 

20 

54  040 

066 

974 

40 

30 

307 

329 

978 

30 

30 

101 

127 

974 

30 

40 

373 

395 

978 

20 

40 

161 

187 

974 

20 

50 

439 

461 

978 

10 

50 

222 

248 

974 

10 

50  0 

.50  504 

.50  527 

.99  978 

0  10 

60  0 

.54  282 

.54  308 

.99  974 

0  0 

8-10 

8-10 

9-10 

8-10 

8-10 

9-10 

1    ri 

log  cos 

log  cot 

log  sin 

II   1 

1    II 

log  cos 

log  cot 

log  sin 

II    t 

88° 


53 


TABLE  V 


NUMERICAL  YALUES 


OF  THE 


TRIGONOMETRIC   FUNCTIONS   OF  ANGLES 

From  0°  to  90° 


FOR  EVERY  MINUTE 


TO  FOUR  PLACES  OF  DECIMALS 


54 


f 

0 

0 

1 

o 

2° 

3 

3 

4° 

1 

sin 

COS 

sin 

COS 

sin   COS 

sin 

COS 

sin 

cos 

0 

.0000 

1.000 

.0175 

.9998 

.0349  .9994 

.0523 

.9986 

.0698 

.9976 

60 

1 

03 

.000 

77 

98 

52    94 

26 

86 

0700 

75 

59 

2 

06 

.000 

80 

98 

55    94 

29 

86 

03 

75 

58 

3 

09 

.000 

83 

98 

58    94 

32 

86 

06 

75 

57 

4 

12 

.000 

86 

98 

61    93 

35 

86 

09 

75 

56 

6 

.0015 

1.000 

.0189 

.9998 

.0364  .9993 

.0538 

.9986 

.0712 

.9975 

55 

6 

17 

.000 

92 

98 

66    93 

41 

85 

15 

74 

54 

7 

20 

.000 

95 

98 

69   93 

44 

85 

18 

74 

53 

8 

23 

.000 

98 

98 

72    93 

47 

85 

21 

74 

52 

9 

26 

.000 

0201 

98 

75    93 

50 

85 

24 

74 

51 

10 

.0029 

1.000 

.0204 

.9998 

.0378  .9993 

.0552 

.9985 

.0727 

.9974 

50 

11 

32 

.000 

07 

98 

81    93 

55 

85 

29 

73 

49 

12 

35 

.000 

09 

98 

84   93 

58 

84 

32 

73 

48 

13 

38 

.000 

12 

98 

87   93 

61 

84 

35 

73 

47 

14 

41 

.000 

15 

98 

90    92 

64 

84 

38 

73 

46 

15 

.0044 

1.000 

.0218 

.9998 

.0393  .9992 

.0567 

.9984 

.0741 

.9973 

45 

16 

47 

.000 

21 

98 

96    92 

70 

84 

44 

72 

44 

17 

49 

.000 

24 

97 

98    92 

73 

84 

47 

72 

43 

18 

52 

.000 

27 

97 

0401    92 

76 

83 

50 

72 

42 

19 

55 

.000 

30 

97 

04    92 

79 

83 

53 

72 

41 

20 

.0058 

1.000 

.0233 

.9997 

.0407  .9992 

.0581 

.9983 

.0756 

.9971 

40 

21 

61 

.000 

36 

97 

10    92 

84 

83 

58 

71 

39 

22 

64 

.000 

39 

97 

13    91 

87 

83 

61 

71 

38 

23 

67 

.000 

41 

97 

16   91 

90 

83 

64 

71 

37 

24 

70 

.000 

44 

97 

19    91 

93 

82 

67 

71 

36 

25 

.0073 

1.000 

.0247 

.9997 

,  .0422  .9991 

.0596 

.9982 

.0770 

.9970 

35 

26 

76 

.000 

50 

97 

25    91 

99 

82 

73 

70 

34 

27 

79 

.000 

53 

97 

27    91 

0602 

82 

76 

70 

33 

28 

81 

.000 

56 

97 

30   91 

05 

82 

79 

70 

32 

29 

84 

.000 

59 

97 

33   91 

08 

82 

82 

69 

31 

30 

.0087 

1.000 

.0262 

.9997 

.0436  .9990 

.0610 

.9981 

.0785 

.9969 

30 

31 

90 

.000 

65 

96 

39    90 

13 

81 

87 

69 

29 

32 

93 

.000 

68 

96 

42    90 

16 

81 

90 

69 

28 

33 

96 

.000 

70 

96 

45    90 

19 

81 

93 

68 

27 

34 

99 

.000 

73 

96 

48   90 

22 

81 

96 

68 

26 

35 

.0102 

.9999 

.0276 

.9996 

.0451  .9990 

.0625 

.9980 

.0799 

.9968 

'25 

36 

05 

99 

79 

96 

54    90 

28 

80 

0802 

68 

24 

37 

08 

99 

82 

96 

57   90 

31 

80 

05 

68' 

23 

38 

11 

99 

85 

96 

59   89 

34 

80 

08 

67 

22 

39 

13 

99 

88 

96 

62    89 

37 

80 

11 

67 

21 

40 

.0116 

.9999 

.0291 

.9996 

.0465  .9989 

.0640 

.9980 

.0814 

.9967 

20 

41 

19 

99 

94 

96 

68    89 

42 

79 

16 

67 

19 

42 

22 

99 

97 

96 

71    89 

45 

79 

19 

66 

18 

43 

25 

99 

0300 

96 

74   89 

48 

79 

22 

66 

17 

44 

28 

99 

02 

95 

77   89 

51 

79 

25 

66 

16 

45 

.0131 

.9999 

.0305 

.9995 

.0480  .9988 

.0654 

.9979 

.0828 

.9966 

15 

46 

34 

99 

08 

95 

83   88 

57 

78 

31 

65 

14 

47 

37 

99 

11 

95 

86   88 

60 

78 

34 

65 

13 

48 

40 

99 

14 

95 

88   88 

63 

78 

37 

65 

12 

49 

43 

99 

17 

95 

91    88 

66 

78 

40 

65 

11 

50 

.0145 

.9999 

.0320 

.9995 

.0494  .9988 

.0669 

.9978 

.0843 

.9964 

10 

51 

48 

99 

23 

95 

97   88 

71 

77 

45 

64 

9 

52 

51 

99 

26 

95 

0500   87 

74 

77 

48 

64 

8 

53 

54 

99 

29 

95 

03   87 

77 

77 

51 

64 

7 

54 

57 

99 

32 

95 

06   87 

80 

77 

54 

63 

6 

55 

.0160 

.9999 

.0334 

.9994 

.0509  .9987 

.0683 

.9977 

.0857 

.9963 

6 

56 

63 

99 

37 

94 

12   87 

86 

76 

60 

63 

4 

57 

66 

99 

40 

94 

15    87 

89 

76 

63 

63 

3 

58 

69 

99 

43 

94 

18   87 

92 

76 

66 

62 

2 

59 

72 

99 

46 

94 

20   86 

95 

76 

69 

62 

1 

60 

.0175 

.9998 

.0349 

.9994 

.0523  .9986 

.0698 

.9976 

.0872 

.9962 

0 

cos 

sin 

cos 

sin 

COS   sin 

COS 

sin 

COS 

sin 

1 

89° 

88 

0 

87° 

86 

° 

85 

o 

f 

55 


1 

5° 

6° 

70 

8° 

9° 

t 

sin   cos 

sin   cos 

sin   cos 

sin   cos 

sin   cos 

0 

.0872  .9962 

.1045  .9945 

.1219  .9925 

.1392  .9903 

.1564  .9877 

60 

1 

74    62 

48    45 

22    25 

95    02 

67    76 

59 

2 

77    61 

51    45 

24    25 

97    02 

70    76 

58 

3 

80    61 

54    44 

27    24 

1400    01 

73    76 

57 

4 

83    61 

57    44 

30    24 

03    01 

76    75 

56 

5 

.0886  .9961 

.1060  .9944 

.1233  .9924 

.1406  .9901 

.1579  .9875 

55 

6 

89    60 

63    43 

36    23 

09    00 

82    74 

54 

7 

92    60 

66    43 

39    23 

12    00 

84    74 

53 

8 

95    60 

68    43 

42    23 

15  9899 

87    73 

52 

9 

98    60 

71    42 

45    22 

18    99 

90   73 

51 

10 

.0901  .9959 

.1074  .9942 

.1248  .9922 

.1421  .9899 

.1593  .9872 

50 

11 

03    59 

77    42 

50    22 

23    98 

96    72 

49 

12 

06    59 

80    42 

53    21 

26    98 

99    71 

48 

13 

09    59 

83    41 

56    21 

29    97 

1602    71 

47 

14 

12    58 

86    41 

59    20 

32    97 

05    70 

46 

15 

.0915  .9958 

.1089  .9941 

.1262  .9920 

.1435  .9897 

.1607  .9870 

45 

16 

18    58 

92    40 

65    20 

38   96 

10    69 

44 

17 

21    58 

94    40 

68    19 

41    96 

13    69 

43 

18 

24    57 

97    40 

71    19 

44  •   95 

16    69 

42 

19 

27    57 

1100    39 

74    19 

46    95 

19    68 

41 

20 

.0929  .9957 

.1103  .9939 

.1276  .9918 

.1449  .9894 

.1622  .9868 

40 

21 

32    56 

06    39 

79    18 

52    94 

25    67 

39 

22 

35    56 

09    38 

82    17 

55    94 

28    67 

38 

23 

38    56 

12    38 

85    17 

58    93 

30    66 

37 

24 

41    56 

15    38 

88    17 

61    93 

33        66 

36 

25 

.0944  .9955 

.1118  .9937 

.1291  .9916 

.1464  .9892 

.1636  .9865 

35 

26 

47    55 

20    37 

94    16 

67    92 

39    65 

34 

27 

50   55 

23    37 

97    16 

69    91 

42    64 

33 

28 

53    55 

26    36 

.  99    15 

72    91 

45    64 

31 

29 

56    54 

29    36 

1302    15 

75    91 

48    63 

31 

30 

.0958  .9954 

.1132  .9936 

.1305  .9914 

.1478  .9890 

.1650  .9863 

30 

31 

61    54 

35    35 

08    14 

81    90 

53    62 

29 

32 

64    53 

38   35 

11    14 

84    89 

56    62 

28 

33 

67    53 

41    35 

14    13 

87    89 

59    61 

27 

34 

70    53 

44    34 

17    13 

90    88 

62    61 

26 

35 

.0973  .9953 

.1146  .9934 

.1320  .9913 

.1492  .9888 

.1665  .9860 

25 

36 

76    52 

49    34 

23    12 

95    88 

68    60 

24 

37 

79    52 

52    33 

25    12 

98    87 

71    59 

23 

38 

.   82    52 

55    33 

28    11 

1501    87 

73    59 

22 

39 

85    51 

58   33 

31    11 

04   86 

76    59 

21 

40 

.0987  .9951 

.1161  .9932 

.1334  .9911 

.1507  .9886 

.1679  .9858 

20 

41 

90   51 

64    32 

37    10 

10   85 

82    58 

19 

42 

93   51 

67    32 

40    10 

13    85 

85    57 

18 

43 

96    50 

70    31 

43    09 

15    84 

88    57 

17 

44 

99    50 

72    31 

46   09 

18    84 

91    56 

16 

45 

.1002  .9950 

.1175  .9931 

.1349  .9909 

.1521  .9884 

.1693  .9856 

15 

46 

05    49 

78   30 

51    08 

24    83 

96    55 

14 

47 

08    49 

81    30 

54    08 

27    83 

99    55 

13 

48 

11    49 

84   30 

57    07 

30    82 

1702    54 

12 

49 

13    49 

87    29 

60   07 

33        82 

05    54 

11 

50 

.1016  .9948 

.1190  .9929 

.1363  .9907 

.1536  .9881 

.1708  .9853 

10 

51 

19    48 

93    29 

66   06 

38   81 

11    53 

9 

52 

22    48 

96    28 

69   06 

41    80 

14    52 

8 

53 

25    47 

98    28 

72    05 

44    80 

16    52 

7 

54 

28    47 

1201    28 

74   05 

47   80 

19    51 

6 

55 

.1031  .9947 

.1204  .9927 

.1377  .9905 

.1550  .9879 

.1722  .9851 

5 

56 

34    46 

07    27 

80   04 

53    79 

25    50 

4 

57 

37   46 

10   27 

83   04 

56    78 

28    50 

3 

58 

39    46 

13    26 

86   03 

59   78 

31    49 

2 

59 

42    46 

16    26 

89   03 

61    77 

34    49 

1 

60 

.1045  .9945 

.1219  .9925 

.1392  .9903 

.1564  .9877 

.1736  .9848 

0 

cos   sin 

cos   sin 

cos   sin 

cos   sin 

cos   sin 

f 

84° 

83° 

82° 

81° 

80° 

' 

56 


1 

10° 

11° 

12° 

13° 

14° 

f 

sin   cos 

sin   cos 

sin   cos 

sm   cos 

sin   cos 

0 

.1736  .9848 

.1908  .9816 

.2079  .9781 

.2250  .9744 

.2419  .9703 

60 

1 

39   48 

11    16 

82    81 

52    43 

22    02 

59 

2 

42    47 

14    15 

85    80 

55    42 

25    02 

58 

3 

45    47 

17    15 

88    80 

58    42 

28    01 

57 

4 

48   46 

20    14 

90    79 

61    41 

31    00 

56 

5 

.1751  .9846 

.1922  .9813 

.2093  .9778 

.2264  .9740 

.2433  .9699 

55 

6 

54    45 

25    13 

96    78 

67    40 

36    99 

54 

7 

57    45 

28    12 

99    77 

69    39 

39    98 

53 

8 

59    44 

31    12 

2102    77 

72    38 

42    97 

52 

9 

62    43 

34    11 

05    76 

75    38 

45    97 

51 

10 

.1765  .9843 

.1937  .9811 

.2108  .9775 

.2278  .9737 

.2447  .9696 

50 

11 

68    42 

39    10 

10    75 

81    36 

50    95 

49 

12 

71    42 

42    10 

13    74 

84    36 

53    94 

48 

13 

74    41 

45    09 

16    74 

86    35 

56   94 

47 

14 

77    41 

48    08 

19   73 

89    34 

59    93 

46 

15 

.1779  .9840 

.1951  .9808 

.2122  .9772 

.2292  .9734 

.2462  .9692 

45 

16 

82'   40 

54    07 

25    72 

95    33 

64    92 

44 

17 

85    39 

57   07 

27    71 

98    32 

67    91 

43 

18 

88    39 

59'   06 

30   70 

2300    32 

70    90 

42 

19 

91    38 

62   06 

33        70 

03    31 

73    89 

41 

20 

.1794  .9838 

.1965  .9805 

.2136  .9769 

.2306  .9730 

.2476  .9689 

40 

21 

97   37 

68    04 

39    69 

09    30 

78    88 

39 

22 

99   37 

71    04 

42    68 

12    29 

81    87 

38 

23 

1802    36 

74   03 

45    67 

15    28 

84    87 

37 

24 

05    36 

77   03 

47    67 

17    28 

87    86 

36 

25 

.1808  .9835 

.1979  .9802 

.2150  .9766 

.2320  .9727 

.2490  .9685 

35 

26 

11    35 

82    02 

53    65 

23    26 

93    84 

34 

27 

14    34 

85    01 

56    65 

26    26 

95    84 

33 

28 

17    34 

88    00 

59    64 

29    25 

98    83 

32 

29 

19    33 

91    00 

62    64 

32    24 

2501    82 

31 

30 

.1822  .9833 

.1994  .9799 

.2164  .9763 

.2334,  .9724 

.2504  .9681 

30 

31 

25    32 

97    99 

67    62 

37    23 

07    81 

29 

32 

28    31 

99    98 

70    62 

40    22 

09    80 

28 

33 

31    31 

2002    98 

73    61 

43    22 

12    79 

27 

34 

34   30 

05    97 

76   60 

46    21 

15    79 

26 

35 

.1837  .9830 

.2008  .9796 

.2179  .9760 

.2349  .9720 

.2518  .9678 

25 

36 

40    29 

11    96 

81    59 

51    20 

21    77 

24 

37 

42    29 

14    95 

84   59 

54    19 

24    76 

23 

38 

45    28 

16   95 

87   58 

57    18 

26    76 

22 

39 

48    28 

19   94 

90   57 

60   18 

29    75 

21 

40 

.1851  .9827 

.2022  .9793 

.2193  .9757 

.2363  .9717 

.2532  .9674 

20 

41 

54    27 

25    93 

96   56 

66   16 

35    73 

19 

42 

57    26 

28    92 

98   55 

68   15 

38    73 

18 

43 

60    26 

31    92 

2201    55 

71    15 

40    72 

17 

44 

62    25 

34   91 

04   54 

74    14 

43    71 

16 

45 

.1865  .9825 

.2036  .9790 

.2207  .9753 

.2377  .9713 

.2546  .9670 

15 

46 

68    24 

39   90 

10   53 

80    13 

49    70 

14 

47 

71    23 

42    89 

13    52 

83    12 

52    69 

13 

48 

74    23 

45    89 

15    51 

85    11 

54    68 

12 

49 

77    22 

48    88 

18   51 

88    11 

57    67 

11 

50 

.1880  .9822 

.2051  .9787 

.2221  .9750 

.2391  .9710 

.2560  .9667 

10 

51 

82    21 

54   87 

24    50 

94   09 

63    66 

9 

52 

85    21 

56   86 

27    49 

97   09 

66    65 

8 

53 

88    20 

59    86 

30   48 

99    08 

69    65 

7 

54 

91    20 

62    85 

33        48 

2402    07 

71    64 

6 

65 

.1894  .9819 

.2065  .9784 

.2235  .9747 

.2405  .9706 

.2574  .9663 

5 

56 

97    18 

68    84 

38   46 

08    06 

77    62 

4 

57 

1900    18 

71    83 

41    46 

11    05 

80   62 

3 

58 

02    17 

73   83 

44   45 

14    04 

83    61 

2 

59 

05    17 

76   82 

47    44 

16   04 

85    60 

1 

60 

.1908  .9816 

.2079  .9781 

.2250  .9744 

.2419  .9703 

.2588  .9659 

0 

cos   sin 

cos   sin 

cos   sin 

cos   sin 

cos   sin 

1 

79° 

78° 

77° 

76° 

75° 

f 

57 


f 

15 

o 

16° 

17° 

18° 

19° 

t 

sin 

COS 

sin   cos 

sin   cos 

sin   cos 

sin   cos 

0 

.2588 

.9659 

.2756  .9613 

.2924  .9563 

.3090  .9511 

.3256  .9455 

60 

1 

91 

59 

59    12 

26    62 

93    10 

58    54 

59 

2 

94 

58 

62    11 

29    61 

96   09 

61    53 

58 

3 

97 

57 

65    10 

32    60 

98    08 

64    52 

57 

4 

99 

56 

68    09 

35    60 

3101    07 

67    51 

56 

5 

.2602 

.9655 

.2770  .9609 

.2938  .9559 

.3104  .9506 

.3269  .9450 

55 

6 

05 

55 

73    08 

40    58 

07    05 

72    49 

54 

7 

08 

54 

76    07 

43    57 

10    04 

75    49 

53 

8 

11 

53 

79    06 

46    56 

12    03 

78   48 

52 

9 

13 

52 

82    05 

49    55 

15    02 

80   47 

51 

10 

.2616 

.9652 

.2784  .9605 

.2952  .9555 

.3118  .9502 

.3283  .9446 

50 

u 

19 

51 

87    04 

54    54 

21    01 

86   45 

49 

12 

22 

50 

90    03 

57    53 

23  9500 

89    44 

48 

13 

25 

49 

93    02 

60    52 

26  9499 

91    43 

47 

14 

28 

49 

95    01 

63    51 

29    98 

94    42 

46 

15 

.2630 

.9648 

.2798  .9600 

.2965  .9550 

.3132  .9497 

.3297  .9441 

45 

16 

33 

47 

2801    00 

68   49 

34    96 

3300   40 

44 

17 

36 

46 

04  9599 

71    48 

37   95 

02    39 

43 

18 

39 

46 

07    98 

74    48 

40    94 

05    38 

42 

19 

42 

45 

09    97 

77    47 

43    93 

08   37 

41 

20 

.2644 

.9644 

.2812  .9596 

.2979  .9546 

.3145  .9492 

.3311  .9436 

40 

21 

47 

43 

15    96 

82    45 

48    92 

13   35 

39 

22 

50 

42 

18    95 

85    44 

51    91 

16   34 

38 

23 

53 

42 

21    94 

•  88    43 

54    90 

19   33 

37 

24 

56 

41 

23    93 

90    42 

56    89 

22    32 

36 

25 

.2658 

.9640 

.2826  .9592 

.2993  .9542 

.3159  .9488 

.3324  .9431 

35 

26 

61 

39 

29    91 

96   41 

62    87 

27    30 

34 

27 

64 

39 

32    91 

99    40 

65    86 

30    29 

33 

28 

67 

38 

35    90 

3002    39 

68    85 

33    28 

32 

29 

70 

37 

37    89 

04    38 

70   84 

35    27 

31 

30 

.2672 

.9636 

.2840  .9588 

.3007  .9537 

.3173  .9483 

.3338  .9426 

30 

31 

75 

36 

43    87 

10   36 

76    82 

41    25 

29 

32 

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0 

cos 

sin 

cos 

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1 

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sin   cos 

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60 

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94    83 

50    05 

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55 

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6 

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50 

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67   47 

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25 

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78   42 

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0 

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14.3007 

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39 

26 

6875 

64 

6223 

08 

5607 

57 

5023 

11 

4469 

21 

40 

.5930 

1.6864 

.6168 

1.6212 

.6412 

1.5597 

.6661 

1.5013 

.6916 

1.4460 

20 

41 

34 

6853 

72 

6202 

16 

5587 

65 

5004 

20 

4451 

19 

42 

38 

6842 

76 

6191 

20 

5577 

69 

4994 

24 

4442 

18 

43 

42 

6831 

80 

6181 

24 

5567 

73 

4985 

29 

4433 

17 

44 

45 

6820 

84 

6170 

28 

5557 

78 

4975 

33 

4424 

16 

45 

.5949 

1.6808 

.6188 

1.6160 

.6432 

1.5547 

.6682 

1.4966 

.6937 

1.4415 

15 

46 

53 

6797 

92 

6149 

36 

5537 

86 

4957 

42 

4406 

14 

47 

57 

6786 

96 

6139 

40 

5527 

90 

4947 

46 

4397 

13 

48 

61 

6775 

6200 

6128 

45 

5517 

94 

4938 

50 

4388 

12 

49 

65 

6764 

04 

6118 

49 

5507 

99 

4928 

54 

4379 

11 

50 

.5969 

1.6753 

.6208 

1.6107 

.6453 

1.5497 

.6703 

1.4919 

.6959 

1.4370 

10 

51 

73 

6742 

12 

6097 

57 

5487 

07 

4910 

63 

4361 

9 

52 

77 

6731 

16 

6087 

61 

5477 

11 

4900 

67 

4352 

8 

53 

81 

6720 

20 

6076 

65 

5468 

15 

4891 

72 

4344 

7 

54 

85 

6709 

24 

6066 

69 

5458 

20 

4882 

76 

4335 

6 

55 

.5989 

1.6698 

.6228 

1.6055 

.6473 

1.5448 

.6724 

1.4872 

.6980 

1.4326 

5 

56 

93 

6687 

33 

6045 

78 

5438 

28 

4863 

85 

4317 

4 

57 

97 

6676 

37 

6034 

82 

5428 

32 

4854 

89 

4308 

3 

58 

6001 

6665 

41 

6024 

86 

5418 

37 

4844 

93 

4299 

2 

59 

05 

6654 

45 

6014 

90 

5408 

41 

4835 

98 

4290 

1 

60 

.6009 

1.6643 

.6249 

1.6003 

.6494 

1.5399 

.6745 

1.4826 

.7002 

1.4281 

0 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

1 

f 

59° 

58° 

57° 

56° 

55° 

sin,  cos 
0°-9° 

70 

f 

35° 

36° 

37° 

38° 

39° 

f 

.0000 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

.9848 

0 

.7002 

1.4281 

.7265 

1.3764 

.7536 

1.3270 

.7813 

1.2799 

.8098 

1.2349 

60 

80°-89^ 

1 

06 
11 

4273 
4264 

70 
74 

3755 
3747 

40 
45 

3262 
3254 

18 
22 

2792 

2784 

8103 
07 

2342 

59 

2 

2334 

58 

sin,  cos 

3 

15 

4255 

79 

3739 

49 

3246 

27 

2776 

12 

2327 

57 

10°-19° 

4 

19 

4246 

83 

3730 

54 

3238 

32 

2769 

17 

2320 

56 

.1736 
.9397 
700-79° 

5 

.7024 

1.4237 

.7288 

1.3722 

.7558 

1.3230 

.7836 

1.2761 

.8122 

1.2312 

55 

6 

7 

28 
32 

4229 
4220 

92 

97 

3713 
3705 

63 
68 

3222 
3214 

41 
46 

2753 
2746 

27 
32 

2305 
2298 

54 
53 

8 

37 

4211 

7301 

3697 

72 

3206 

50 

2738 

36 

2290 

52 

sin,  COS 

9 

41 

4202 

06 

3688 

77 

3198 

55 

2731 

41 

2283 

51 

20°-29 

.3420 

10 

.7046 

1.4193 

.7310 

1.3680 

.7581 

1.3190 

.7860 

1.2723 

.8146 

1.2276 

50 

11 

50 

4185 

14 

3672 

86 

3182 

65 

2715 

51 

2268 

49 

.8660 
60°-69 

12 

54 

4176 

19 

3663 

90 

3175 

69 

2708 

56 

2261 

48 

13 
14 

59 
63 

4167 
4158 

23 

28 

3655 
3647 

95 
7600 

3167 
3159 

74 
79 

2700 
2693 

61 
65 

2254 
2247 

47 
46 

sin,  CO 

3D°-39 

.5000 

.7660 

5a°-69 

15 

.7067 

1.4150 

.7332 

1.3638 

.7604 

1.3151 

.7883 

1.2685 

.8170 

1.2239 

45 

16 

72 

4141 

37 

3630 

09 

3143 

88 

2677 

75 

2232 

44 

17 
18 

76 

80 

4132 
4124 

41 
46 

3622 
3613 

13 
18 

3135 
3127 

93 

98 

2670 
2662 

80 

85 

2225 
2218 

43 
42 

19 

85 

4115 

50 

3605 

23 

3119 

7902 

2655 

90 

2210 

41 

sin,  coe 

400-44 

.6428 

.7071 

45°-49 

20 

.7089 

1.4106 

.7355 

1.3597 

.7627 

1.3111 

.7907 

1.2647 

.8195 

1.2203 

40 

21 

94 

4097 

59 

3588 

32 

3103 

12 

2640 

99 

2196 

39 

22 

98 

4089 

64 

3580 

36 

3095 

16 

2632 

8204 

2189 

38 

23 

7102 

4080 

68 

3572 

41 

3087 

21 

2624 

09 

2181 

37 

24 

07 

4071 

73 

3564 

46 

3079 

26 

2617 

14 

2174 

36 

25 

.7111 

1.4063 

.7377 

1.3555 

.7650 

1.3072 

.7931 

1.2609 

.8219 

1.2167 

35 

tan,  CO 

26 

15 

4054 

82 

3547 

55 

3064 

35 

2602 

24 

2160 

34 

0°-4° 

27 

20 

4045 

86 

3539 

59 

3056 

40 

2594 

29 

2153 

33 

.0000 

28 

24 

4037 

91 

3531 

64 

3048 

45 

2587 

34 

2145 

32 

11.43 

29 

29 

4028 

95 

3522 

69 

3040 

50 

2579 

38 

2138 

31 

«fio  fi*- 

30 

.7133 

1.4019 

.7400 

1.3514 

.7673 

1.3032 

.7954 

1.2572 

.8243 

1.2131 

30 

31 

37 

4011 

04 

3506 

78 

3024 

59 

2564 

48 

2124 

29 

tan, 

32 

42 

4002 

09 

3498 

83 

3017 

64 

2557 

53 

2117 

28 

5°-V 

33 

46 

3994 

13 

3490 

87 

3009 

69 

2549 

58 

2109 

27 

.0875 

34 

51 

3985 

18 

3481 

92 

3001 

73 

2542 

63 

2102 

26 

3.732 

36 

.7155 

1.3976 

.7422 

1.3473 

.7696 

1.2993 

.7978 

1.2534 

.8268 

1.2095 

25 

•yfio 

36 

59 

3968 

27 

3465 

7701 

2985 

83 

2527 

73 

2088 

24 

tan,  CO 
15°-24 

.2679 

37 

64 

3959 

31 

3457 

06 

2977 

88 

2519 

78 

2081 

23 

38 

68 

3951 

36 

3449 

10 

2970 

92 

2512 

83 

2074 

22 

39 

73 

3942 

40 

3440 

15 

2962 

97 

2504 

87 

2066 

21 

2.144 

40 

.7177 

1.3934 

.7445 

1.3432 

.7720 

1.2954 

.8002 

1.2497 

.8292 

1.2059 

20 

65°-7'' 

41 

81 

3925 

49 

3424 

24 

2946 

07 

2489 

97 

2052 

19 

42 

86 

3916 

54 

3416 

29 

2938 

12 

2482 

8302 

2045 

18 

tan,  ( 
25°-2 

43 

90 

3908 

58 

3408 

34 

2931 

16 

2475 

07 

2038 

17 

44 

95 

3899 

63 

3400 

38 

2923 

21 

2467 

12 

2031 

16 

.4663 

45 

.7199 

1.3891 

.7467 

1.3392 

.7743 

1.2915 

.8026 

1.2460 

.8317 

1.2024 

15 

1.428 

46 

7203 

3882 

72 

3384 

47 

2907 

31 

2452 

22 

2017 

14 

65°-f 

47 

08 

3874 

76 

3375 

52 

2900 

35 

2445 

27 

2009 

13 

48 

12 

3865 

81 

3367 

57 

2892 

40 

2437 

•  32 

2002 

12 

tan,  CO 

t   49 

17 

3857 

85 

3359 

61 

2884 

45 

2430 

37 

1995 

11 

36°-44 

0   50 

.7221 

1.3848 

.7490 

1.3351 

.7766 

1.2876 

.8050 

1.2423 

.8342 

1.1988 

10 

.7002 

51 

26 

3840 

95 

3343 

71 

2869 

55 

2415 

46 

1981 

9 

1.000 

52 

30 

3831 

99 

3335 

75 

2861 

59 

2408 

51 

1974 

8 

46°-64 

t°  53 

34 

3823 

7504 

3327 

80 

2853 

64 

2401 

56 

1967 

7 

54 

39 

3814 

08 

3319 

85 

2846 

69 

2393 

61 

1960 

6 

65 

.7243 

1.3806 

.7513 

1.3311 

.7789 

1.2838 

.8074 

1.2386 

.8366 

1.1953 

5 

56 

48 

3798 

17 

3303 

94 

2830 

79 

2378 

71 

1946 

4 

57 

52 

3789 

22 

3295 

99 

2822 

83 

2371 

76 

1939 

3 

58 

57 

3781 

26 

3287 

7803 

2815 

88 

2364 

81 

1932 

2 

59 

61 

3772 

31 

3278 

08 

2807 

93 

2356 

86 

1925 

1 

60 

.7265 

1.3764 

.7536 

1.3270 

.7813 

1.2799 

.8098 

1.2349 

.8391 

1.1918 

0 

HIHI 

■ 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

^^^1 

m  ' 

54°     1 

53° 

52° 

51° 

50°     1 

' 

71 


t 

40° 

41° 

42° 

43° 

44° 

t 

tan 

cot 

tan 

cot 

tan 

cot 

tan    cot 

tan 

cot 

0 

.8391 

1.1918 

.8693 

1.1504 

.9004 

1.1106 

.9325  1.0724 

.9657 

1.0355 

60 

1 

96 

1910 

98 

1497 

09 

1100 

31   0717 

63 

0349 

59 

2 

8401 

1903 

8703 

1490 

15 

1093 

36   0711 

68 

0343 

58 

3 

06 

1896 

08 

1483 

.20 

1087 

41   0705 

74 

0337 

57 

4 

11 

1889 

13 

1477 

25 

1080 

47   0699 

79 

0331 

56 

5 

.8416 

1.1882 

.8718 

1.1470 

.9030 

1.1074 

.9352  1.0692 

.9685 

1.0325 

55 

6 

21 

1875 

24 

1463 

36 

1067 

58   0686 

91 

0319 

54 

7 

26 

1868 

29 

1456 

41 

1061 

63   0680 

96 

0313 

53 

8 

31 

1861 

34 

1450 

46 

1054 

69   0674 

9702 

0307 

52 

9 

36 

1854 

39 

1443 

52 

1048 

74   0668 

08 

0301 

51 

10 

.8441 

1.1847 

.8744 

1.1436 

.9057 

1.1041 

.9380  1.0661 

.9713 

1.0295 

50 

11 

46 

1840 

49 

1430 

62 

1035 

85   0655 

19 

0289 

49 

12 

51 

1833 

54 

1423 

67 

1028 

91   0649 

25 

0283 

48 

13 

56 

1826 

59 

1416 

73 

1022 

96   0643 

30 

0277 

47 

14 

61 

1819 

65 

1410 

7« 

1016 

9402   0637 

36 

0271 

46 

15 

.8466 

1.1812 

.8770 

1.1403 

.9083 

1.1009 

.9407  1.0630 

.9742 

1.0265 

45 

16 

71 

1806 

75 

1396 

89 

1003 

13   0624 

47 

0259 

44 

17 

76 

1799 

80 

1389 

94 

0996 

18   0618 

53 

0253 

43 

18 

81 

1792 

85 

13S3 

99 

0990 

24   0612 

59 

0247 

42 

19 

86 

1785 

90 

1376 

9105 

0983 

29   0606 

64 

0241 

41 

20 

.8491 

1.1778 

.8796 

1.1369 

.9110 

1.0977 

.9435  1.0599 

.9770 

1.0235 

40 

21 

96 

1771 

8801 

1363 

15 

0971 

40   0593 

76 

0230 

39 

22 

8501 

1764 

06 

1356 

21 

0964 

46   0587 

81 

0224 

38 

23 

06 

1757 

11 

1349 

26 

0958 

51   0581 

87 

0218 

37 

24 

11 

1750 

16 

1343 

31 

0951 

57   0575 

93 

0212 

36 

25 

.8516 

1.1743 

.8821 

1.1336 

.9137 

1.0945 

.9462  1.0569 

.9798 

1.0206 

35 

26 

21 

1736 

27 

1329 

42 

0939 

68   0562 

9804 

0200 

34 

27 

26 

1729 

32 

1323 

47 

0932 

73   0556 

10 

0194 

33 

28 

31 

1722 

37 

1316 

53 

0926 

79   0550 

16 

0188 

32 

29 

36 

1715 

42 

1310 

58 

0919 

84   0544 

21 

0182 

31 

30 

.8541 

1.1708 

.8847 

1.1303 

.9163 

1.0913 

.9490  1.0538 

.9827 

1.0176 

30 

31 

46 

1702 

52 

1296 

69 

0907 

95   0532 

33 

0170 

29 

32 

51 

1695  • 

58 

1290 

74 

0900 

9501   0526 

38 

0164 

28 

33 

56 

1688 

63 

1283 

79 

0894 

06   0519 

44 

0158 

27 

34 

61 

1681 

68 

1276 

85 

0888 

12   0513 

50 

0152 

26 

35 

.8566 

1.1674 

.8873 

1.1270 

.9190 

1.0881 

.9517  1.0507 

.9856 

1.0147 

25 

36 

71 

1667 

78 

1263 

95 

0875 

23   0501 

61 

0141 

24 

37 

76 

1660 

84 

1257 

9201 

0869 

28   0495 

67 

0135 

23 

38 

81 

1653 

89 

1250 

06 

0862 

34   0489 

73 

0129 

22 

39 

86 

1647 

94 

1243 

12 

0856 

40   0483 

79 

0123 

21 

40 

.8591 

1.1640 

.8899 

1.1237 

.9217 

1.0850 

.9545  1.0477 

.9884 

1.0117 

20 

41 

96 

1633 

8904 

1230 

22 

0843 

51   0470 

90 

0111 

19 

42 

8601 

1626 

10 

1224 

28 

0837 

56   0464 

96 

0105 

18 

43 

06 

1619 

15 

1217 

33 

0831 

62   0458 

9902 

0099 

17 

44 

11 

1612 

20 

1211 

39 

0824 

67   0452 

07 

0094 

16 

45 

.8617 

1.1606 

.8925 

1.1204 

.9244 

1.0818 

.9573  1.0446 

.9913 

1.0088 

15 

46 

22 

1599 

31 

1197 

49 

0812 

78   0440 

19 

0082 

14 

47 

27 

1592 

36 

1191 

55 

0805 

84   0434 

25 

0076 

13 

48 

32 

1585 

41 

1184 

60 

0799 

90   0428 

30 

0070 

12 

49 

37 

1578 

46 

1178 

66 

0793 

95   0422 

36 

0064 

11 

50 

.8642 

1.1571 

.8952 

1.1171 

.9271 

1.0786 

.9601  1.0416 

.9942 

1.0058 

10 

51 

47 

1565 

57 

1165 

76 

0780 

06   0410 

48 

0052 

9 

52 

52 

1558 

62 

1158 

82 

0774 

12   0404 

54 

0047 

8 

53 

57 

1551 

67 

1152 

87 

0768 

18   0398 

59 

0041 

7 

54 

62 

1544 

72 

1145 

93 

0761 

23   0392 

65 

0035 

6 

55 

.8667 

1.1538 

.8978 

1.1139 

.9298 

1.0755 

.9629  1.0385 

.9971 

1.0029 

5 

56 

72 

1531 

83 

1132 

9303 

0749 

34   0379 

77 

0023 

4 

57 

78 

1524 

88 

1126 

09 

0742 

40   0373 

83 

0017 

3 

58 

83 

1517 

94 

1119 

14 

0736 

46  ■  0367 

88 

0012 

2 

59 

88 

1510 

99 

1113 

20 

0730 

51   0361 

94 

0006 

1 

60 

.8693 

1.1504 

.9004 

1.1106 

.9325 

1.0724 

.9657  1.0355 

1.0000 

1.0000 

0 

cot 

tan 

cot 

tan 

cot 

tan 

cot    tan 

cot 

tan 

' 

49° 

48° 

47° 

46° 

45° 

t 

72 


TABLE  VI 

THE  LOGARITHMS  S  . 

iND 

T 

The  angle  a"  being  less  than  7275" 

FORMULAS  FOR  THE  USE  OF 

S  AND 

T 

When  the  angle  A  is  less  than  2°, 

let                             a  =  the  number  of  seconds  in  the  angle  A ; 

then                          S  =  log  sin  a''  —  log  a, 

T  =  log  tan  a''  -  log  a, 

log  cot  a'"  =  -  log  tan  a". 

When  the  angle  A  is  between  88^  and  90°, 

let                           a''  =  the  number  of  seconds  in  the  angle  90° 

-^; 

then             log  cos  ^  =  log  or  +  S, 

log  cot  A  =\oga  -h  T, 

log  tan  A  =  —  log  tan  a'\ 

The  angle  ^  <  2°  or  >  88°, 

when  log  sin  A  or  log  cos  A  <  2.54282  or 

>  1.99974, 

or  when  log  tan  A  or  log  cot  A  <  2.54308  or 

>  1.45692. 

a 

S          log  sin  a" 

a                T          log  tan  a" 

a 

T 

log  tan  a" 

0 

0 

5  146 

2.39  713 

2  409 

6.68  557     _ 

2.06  740 

6.68  557      _ 
200                        4.98  660 

5  424 

6.68  567 

2.41  999 

3  417 

6.68  556     _ 

2.21  920 

6.68  558     _ 
1  726                        3.92  263 

5  689 

6.6S  568 

2.44  072 

3  823 

6.68  555     _ 

2.26  795 

6.68  559      _ 
2  432                        2.07  156 

5  941 

6.68  569 

2.45  955 

4  190 

6.68  555      _ 

2.30  776 

6.68  560 
2  976                        2.15  924 

6184 

6.68  570 

2.47  697 

4  840 

6.68  554     _ 

2.37  038 

6.68  561 
3  434                        2.22  142 

6417 

6.68  571 

2.49  305 

5  414 

6.68  553      _ 

2.41  904 

6.68  562 
3  838                        2.26  973 

6  642 

6.68  572 

2.50  802 

5  932 

6.68  552     _ 

2.45  872 

6.68  563      _ 
4  204                        2.30  930 

6  859 

6.68  573 

2.52  200 

6  408 

6.6S  551      _ 

2.49  223 

6.68  564      _ 
4  540                        2.34  270 

7  070 

6.68  574 

2.53  516 

6  633 

6.68  550     _ 

2.50  721 

6.68  565      _ 
4  699                        2.35  766 

7173 

6.68  57i 

2.54  145 

6  851 

6.68  550      _ 

2.52  125 

6.68  565 
4  853                         2.37167 

7  274 

6.68  575 

2.54  753 

7  267 

a 

6.68  549 

2.54  684 

6.68  566 
5  146                        2.39  713 

S           log  sin  a" 

a                T          log  tan  a" 

a 

T 

log  tan  a" 

ANNOUNCEMENTS 


TEXTBOOKS  IN  MATHEMATICS 

FOR  COLLEGES  AND  UNIVERSITIES 

Anderegg  and  Roe  :  Trigonometry  (Revised  Edition) 

Bailey  and  Woods :  Plane  and  Solid  Analytic  Geometry 

Barker :  Computing  Tables  and  Mathematical  Formulas 

Byerly :  Elements  of  the  Integral  Calculus  (Revised) 

Byerly :  Fourier's  Series 

Byerly :  Generalized  Coordinates 

Clements  :  Problems  in  the  Mathematical  Theory  of  Investment 

Comstock  :  Method  of  Least  Squares 

Durfee :  Elements  of  Plane  Trigonometry 

Eisenhart :  Differential  Geometry  of  Curves  and  Surfaces 

Faunce:  Descriptive  Geometry 

Fine :  College  Algebra 

Glenn :  The  Theory  of  Invariants 

Granville :  Plane  and  Spherical  Trigonometry  and  Tables 

Granville  and  Smith :  Differential  and  Integral  Calculus 

Hall:  Mensuration 

Halsted :  Metrical  Geometry 

Hancock :  Theory  of  Maxima  and  Minima 

Hawkes :  Higher  Algebra 

Hedrick :  Goursat's  Mathematical  Analysis,  Vol.  I 

Volume  II,  Part  I.    Functions  of  a  Complex  Variable 

Volume  II,  Part  II.    Differential  Equations 
Hedrick  and  Kellogg :  Applications  of  the  Calculus  to  Mechanics 
Hooper  and  Wells :  Electrical  Problems 

Ingersoll  and  Zobel :  Mathematical  Theory  of  Heat  Conduction 
Lehmer :  Synthetic  Projective  Geometry 
Leib :  Problems  in  the  Calculus 
Lester :  Integrals  of  Mechanics 
Longley :  Tables  and  Formulas  (Revised  Edition) 
McClenon  and  Rusk:  Elementary  Functions 
Manning :  Non-Euclidean  Geometry 
Maurus :  An  Elementary  Course  in  Differential  Equations 
Osborne :  Examples  of  Differential  Equations 


114a 

GINN  AND   COMPANY  Publishers 


TEXTBOOKS   IN   MATHEMATICS 

FOR  COLLEGES  AND  UNIVERSITIES 

Continued 

Peirce,  B.  O. :  Short  Table  of  Integrals  (Revised) 
Peirce,  B.  O. :  The  Newtonian  Potential  Function 
Pierpont :  Functions  of  a  Complex  Variable 
Pierpont :   Functions  of  Real  Variables,  Volume  I 

Volume  II 
Randall :  Elements  of  Descriptive  Geometry 
Randall :  Shades  and  Shadows,  and  Perspective 
Richardson :   Solid  Geometry 
Shepard :  Problems  in  the  Strength  of  Materials 
Skinner :  Mathematical  Theory  of  Investment 
Slocum  :  Resistance  of  Materials 
Slocum  and  Hancock :   Strength  of  Materials 
Smith  and  Gale :   Elements  of  Analytic  Geometry 
Smith  and  Gale :  Introduction  to  Analytic  Geometry 
Smith  and  Gale :  New  Analytic  Geometry 
Smith  and  Granville  :  Elementary  Analysis 
Smith  and  Longley :  Theoretical  Mechanics 
Taylor :  Elements  of  the  Calculus  (Revised  and  Enlarged) 
Taylor :  Logarithmic  and  Trigonometric  Tables 
Taylor  and  Puryear  :  Plane  and  Spherical  Trigonometry 
Veblen  and  Young :  Projective  Geometry,  Volume  I 

Volume  II 
Wentworth  :  College  Algebra  (Revised  Edition) 
Wentworth :  Trigonometries  (Second  Revised  Edition) 

{^For  list  see  Descriptive  Catalogue) 

Wentworth  and  Smith :  Plane  and  Spherical  Trigonometries 

{For  list  see  Descriptive  Catalogue) 

Wentworth  and  Smith :  Solid  Geometry 

Wilson :  Advanced  Calculus 

Woods  and  Bailey :  A  Course  in  Mathematics,  Volume  I 

Volume  II 
Woods  and  Bailey :  Analytic  Geometry  and  Calculus 

114b 

GINN  AND   COMPANY  Publishers 


BOOKS   OF  CONVENIENCE 
FOR  MATHEMATICIANS 


TABLES  AND  FORMULAS.     For  solving  Numerical  Problems 
in  Analytic  Geometry,  Calculus,  and  Applied  Mathematics 

Compiled  by  William  Raymond  Longi.ey,  Assistant  Professor  of  Mathematics, 
Sheffield  Scientific  School,  Yale  University. 

The  use  of  this  book  promotes  economy  of  time  and  effort.    All 

necessary  tables  and  formulas  are  included,  but  there  is  no  extended 

cumbersome  material. 

COMPUTING  TABLES  AND   MATHEMATICAL 
FORMULAS 

Compiled  by  E.  H.  Barker,  former  Head  of  the  Mathematics  Department,  Poly- 
technic High  School,  Los  Angeles,  Cal.   Narrow  i2mo,  semiiiexible  cloth,  88  pages. 

Students  of  mathematics,  draftsmen,  and  engineers  will  find  all  the 

material  required  easily  accessible  in  this  handy  pocket  manual. 


NOTEBOOKS  FOR  COLLEGE  CLASSES 

By  Robert  K.  Mokitz,  Professor  and  Head  of  the  Department  of  Mathematics  in  the 
University  of  Washington 

COLLEGE  MATHEMATICS  NOTEBOOK 

This  notebook,  of  great  value  to  students  of  mathematics,  physics, 
astronomy,  and  chemistry,  contains  lists  of  important  formulas  from 
algebra,  geometry,  trigonometry,  and  analytics,  one  hundred  sheets  of  co- 
ordinate paper,  seven  two-place  tables,  and  eight  sets  of  standard  graphs. 

COLLEGE  ENGINEERING  NOTEBOOK 

A  TIME-SAVING  notebook  for  students  in  civil,  mechanical,  and  electri- 
cal engineering,  containing  lists  of  important  formulas,  tables,  and  sets  of 
type  curves.  There  are  ninety  sheets  of  rectangular  coordinate  paper  and 
five  sheets  each  of  polar-coordinate  and  logarithmic-coordinate  paper. 


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BOOKS  IN 
HIGHER  MATHEMATICS 

HIGHER  ALGEBRA 

By  Herbert  E.  Havvkes,  Columbia  University 

A  THOROUGH  development  of  college  algebra  that  vi'ill  be  found  especially 
adapted  for  use  in  technical  schools.  The  reasonable  use  of  graphical  methods, 
care  in  finding  the  limit  of  error  in  numerical  computations,  and  the  use  of  tables 
in  extracting  roots  are  all  features  in  accord  with  modern  instruction  in  applied 
mathematics. 

THEORY  OF  FUNCTIONS  OF  REAL  VARIABLES 

By  James  Pierpont,  Yale  University.   Vol.  I,  Vol.  II 

"  A  MOST  admirable  exposition  of  what  in  modern  times  have  come  to  be  re- 
garded as  the  unshakable  foundations  of  analysis.  Hitherto,  in  order  to  gain  a 
knowledge  of  the  best  that  has  been  done  in  the  subject,  it  has  been  necessary 
to  repair  to  foreign  institutions ;  now  it  is  no  longer  necessary  to  have  recourse 
to  foreign  tongues,  thanks  to  Professor  Pierpont's  simple  and  scholarly  presenta- 
tion." —  The  Nation. 

FUNCTIONS  OF  A  COMPLEX  VARIABLE 

By  James  Pierpont,  Yale  University 

Adapted  to  the  needs  both  of  students  of  applied  mathematics  and  of  those 
specializing  in  pure  mathematics.  The  elliptic  functions  and  linear  homogeneous 
differential  equations  of  order  two  are  treated,  and  the  functions  of  Legendre, 
Laplace,  Bessel,  and  Lame  are  studied  in  some  detail. 

MATHEMATICAL  THEORY  OF  INVESTMENT 

By  Ernest  Brown  Skinner,  University  of  Wisconsin 

The  mathematical  material  that  will  prove  most  useful  to  the  modern  educated 
business  man.  The  book  treats  the  theory  of  interest,  both  simple  and  compound, 
the  theory  of  bond  values,  depreciation,  sinking  funds,  the  amortization  of  debts 
by  various  plans,  inheritance  taxes,  old-age  pensions,  and  life  insurance. 

MATHEMATICAL  THEORY  OF  HEAT  CONDUCTION 

By  L.  R.  Ingersoll,  University  of  Wisconsin,  and  O.  J.  Zobel 

A  text  in  Fourier's  Series  and  Heat  Conduction,  presenting  along  with  the 
theory  a  large  number  of  practical  applications  of  special  value  to  geologists  and 
engineers.  These  include  problems  in  the  tempering  of  steels,  freezing  of  con- 
crete, electric  and  thermit  welding,  and  similar  questions.  The  book  presents 
an  excellent  first  course  in  mathematical  physics. 


GINN  AND   COMPANY   Publishers 


UNIVERSITY  or  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed 
This b!lisDUE  on  the  last  date  stamped  below. 


7Nov'45W\ 


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24Ma/54lllf 

V;^'^:  '  1955 10 
26Mar'60BSI 
IN  STACKS 

MAR  12 1960 


JUNl    1960 

REC'D  LD 

13'65-9PM 


LD21-100m-9,'48CB899sl6)476 


.YC  22432 


863773 


UNIVERSITY  OF  CALIFORNIA  UBRARY 


